This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random measurement delays. A new model that describes the random delays is constructed where possible...This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random measurement delays. A new model that describes the random delays is constructed where possible the largest delay is bounded. Based on this new model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. A simulation example shows the effectiveness of the proposed algorithms.展开更多
This article deals with an averaging principle for Caputo fractional stochastic differential equations with compensated Poisson random measure.The main contribution of this article is impose some new averaging conditi...This article deals with an averaging principle for Caputo fractional stochastic differential equations with compensated Poisson random measure.The main contribution of this article is impose some new averaging conditions to deal with the averaging principle for Caputo fractional stochastic differential equations.Under these conditions,the solution to a Caputo fractional stochastic differential system can be approximated by that of a corresponding averaging equation in the sense ofmean square.展开更多
Let D be a convolution semigroup of random measures or point processes on a locally compact second countable T 2space. There is a topological isomorphism from D into a subsemigroup of product topological semigroup (R ...Let D be a convolution semigroup of random measures or point processes on a locally compact second countable T 2space. There is a topological isomorphism from D into a subsemigroup of product topological semigroup (R +,+) N.D is a sequentially stable and D-separable ZH-semigroup, as well as a metrizable, stable and normable Hun semigroup, so it has the corresponding properties. In particular the author has a new and simple proof byZH-semigroup approach or Hun semigroup approach to show that D has property ILID (an infinitesimal array limit is infinitely divisible), and know the Baire types which some subsets of D belong in.展开更多
We study a stochastic Cahn-Hilliard equation driven by a Poisson random measure with Neumann boundary conditions. The global weak solution is established for the equation. Moreover, the existence of a Lyapunov functio...We study a stochastic Cahn-Hilliard equation driven by a Poisson random measure with Neumann boundary conditions. The global weak solution is established for the equation. Moreover, the existence of a Lyapunov function for the equation and an invariant measure associated with the transition semigroup are proved.展开更多
Backward stochastic differential equations (BSDE) are discussed in many papers. However, in those papers, only Brownian motion and Poisson process are considered. In this paper, we consider BSDE driven by continuous l...Backward stochastic differential equations (BSDE) are discussed in many papers. However, in those papers, only Brownian motion and Poisson process are considered. In this paper, we consider BSDE driven by continuous local martingales and random measures.展开更多
In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise....In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).展开更多
In this paper,we present the semi-implicit Euler(SIE)numerical solution for stochastic pantograph equations with jumps and prove that the SIE approximation solution converges to the exact solution in the mean-square...In this paper,we present the semi-implicit Euler(SIE)numerical solution for stochastic pantograph equations with jumps and prove that the SIE approximation solution converges to the exact solution in the mean-square sense under the Local Lipschitz condition.展开更多
This paper provides a contemporary overview of phase retrieval problem with PhaseLift algorithm and summarizes theoretical results which have been derived during the past few years.Based on the lifting technique,the p...This paper provides a contemporary overview of phase retrieval problem with PhaseLift algorithm and summarizes theoretical results which have been derived during the past few years.Based on the lifting technique,the phase retrieval problem can be transformed into the low rank matrix recovery problem and then be solved by convex programming known as PhaseLift.Thus,stable guarantees for such problem have been gradually established for measurements sampled from sufficiently random distribution,for instance,the standard normal distribution.Further,exact recovery results have also been set up for masked Fourier measurements which are closely related to practical applications.展开更多
The open set condition is the weakest condition hitherto in multifractal decomposition on the recursive sets. This paper deals with certain recursive fractals which have no relevence to the separation condition and gi...The open set condition is the weakest condition hitherto in multifractal decomposition on the recursive sets. This paper deals with certain recursive fractals which have no relevence to the separation condition and gives their multifractal decomposition.展开更多
In this article, we give a new proof of the Itôformula for some integral processes related to the space-time Lévy noise introduced in [1] [2] as an alternative for the Gaussian white noise perturbing an...In this article, we give a new proof of the Itôformula for some integral processes related to the space-time Lévy noise introduced in [1] [2] as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two applications of this result, which are useful in the study of SPDEs driven by a space-time Lévy noise with finite variance: a maximal inequality for the p-th moment of the stochastic integral, and the Itôrepresentation theorem leading to a chaos expansion similar to the Gaussian case.展开更多
Both necessary and sufficient maximum principles for optimal control of stochastic systemwith random jumps consisting of forward and backward state variables are proved.The control variableis allowed to enter both dif...Both necessary and sufficient maximum principles for optimal control of stochastic systemwith random jumps consisting of forward and backward state variables are proved.The control variableis allowed to enter both diffusion and jump coefficients.The result is applied to a mean-varianceportfolio selection mixed with a recursive utility functional optimization problem.Explicit expressionof the optimal portfolio selection strategy is obtained in the state feedback form.展开更多
The problem of reconstructing n-by-n structured matrix signal X=(x1,...,xn)via convex optimization is investigated,where each column xj is a vector of s-sparsity and all columns have the same l1-norm value.In this pap...The problem of reconstructing n-by-n structured matrix signal X=(x1,...,xn)via convex optimization is investigated,where each column xj is a vector of s-sparsity and all columns have the same l1-norm value.In this paper,the convex programming problem was solved with noise-free or noisy measurements.The uniform sufficient conditions were established which are very close to necessary conditions and non-uniform conditions were also discussed.In addition,stronger conditions were investigated to guarantee the reconstructed signal’s support stability,sign stability and approximation-error robustness.Moreover,with the convex geometric approach in random measurement setting,one of the critical ingredients in this contribution is to estimate the related widths’bounds in case of Gaussian and non-Gaussian distributions.These bounds were explicitly controlled by signal’s structural parameters r and s which determined matrix signal’s column-wise sparsity and l1-column-flatness respectively.This paper provides a relatively complete theory on column-wise sparse and l1-column-flat matrix signal reconstruction,as well as a heuristic foundation for dealing with more complicated high-order tensor signals in,e.g.,statistical big data analysis and related data-intensive applications.展开更多
For maritime radiation source target tracking in particular electronic counter measures(ECM)environment,there exists two main problems which can deteriorate the tracking performance of traditional approaches.The frs...For maritime radiation source target tracking in particular electronic counter measures(ECM)environment,there exists two main problems which can deteriorate the tracking performance of traditional approaches.The frst problem is the poor observability of the radiation source.The second one is the measurement uncertainty which includes the uncertainty of the target appearing/disappearing and the detection uncertainty(false and missed detections).A novel approach is proposed in this paper for tracking maritime radiation source in the presence of measurement uncertainty.To solve the poor observability of maritime radiation source target,using the radiation source motion restriction,the observer altitude information is incorporated into the bearings-only tracking(BOT)method to obtain the unique target localization.Then the two uncertainties in the ECM environment are modeled by the random fnite set(RFS)theory and the Bernoulli fltering method with the observer altitude is adopted to solve the tracking problem of maritime radiation source in such context.Simulation experiments verify the validity of the proposed approach for tracking maritime radiation source,and also demonstrate the superiority of the method compared with the traditional integrated probabilistic data association(IPDA)method.The tracking performance under different conditions,particularly those involving different duration of radiation source opening and switching-off,indicates that the method to solve our problem is robust and effective.展开更多
This paper discusses the H∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including i...This paper discusses the H∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including internal stability and external stability, which enables to prove the bounded real lemma for the systems. By means of Riccati equations, infinite horizon linear stochastic state-feedback H∞ control design is also extended to such systems.展开更多
Backward doubly stochastic differential equations driven by Brownian motions and Poisson process (BDSDEP) with non-Lipschitz coefficients on random time interval are studied. The probabilistic interpretation for the...Backward doubly stochastic differential equations driven by Brownian motions and Poisson process (BDSDEP) with non-Lipschitz coefficients on random time interval are studied. The probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations (SPDIEs) is treated with BDSDEP. Under non-Lipschitz conditions, the existence and uniqueness results for measurable solutions to BDSDEP are established via the smoothing technique. Then, the continuous depen- dence for solutions to BDSDEP is derived. Finally, the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given.展开更多
In this paper, we establish existence and uniqueness of the mild solutions to a class of neutral stochastic evolution equations driven by Poisson random measures in some Hilbert space. Moreover, we adopt the Faedo-Gal...In this paper, we establish existence and uniqueness of the mild solutions to a class of neutral stochastic evolution equations driven by Poisson random measures in some Hilbert space. Moreover, we adopt the Faedo-Galerkin scheme to approximate the solutions.展开更多
This paper discusses mean-field backward stochastic differentiM equations (mean-field BS- DEs) with jumps and a new type of controlled mean-field BSDEs with jumps, namely mean-field BSDEs with jumps strongly coupled...This paper discusses mean-field backward stochastic differentiM equations (mean-field BS- DEs) with jumps and a new type of controlled mean-field BSDEs with jumps, namely mean-field BSDEs with jumps strongly coupled with the value function of the associated control problem. The authors first prove the existence and the uniqueness as well as a comparison theorem for the above two types of BSDEs. For this the authors use an approximation method. Then, with the help of the notion of stochastic backward semigroups introduced by Peng in 1997, the authors get the dynamic programming principle (DPP) for the value functions. Furthermore, the authors prove that the value function is a viscosity solution of the associated nonlocal Hamilton-Jacobi-Bellman (HJB) integro-partial differential equation, which is unique in an adequate space of continuous functions introduced by Barles, et al. in 1997.展开更多
For stochastic reaction-diffusion equations with Levy noises and non-Lipschitz reaction terms,we prove that W\H transportation cost inequalities hold for their invariant probability measures and for their process-leve...For stochastic reaction-diffusion equations with Levy noises and non-Lipschitz reaction terms,we prove that W\H transportation cost inequalities hold for their invariant probability measures and for their process-level laws on the path space with respect to the L1-metrie.The proofs are based on the Galerkin approximations.展开更多
We prove a general version of the stochastic Fubini theorem for stochastic integrals of Banach space valued processes with respect to compensated Poisson random measures under weak integrability assumptions, which ext...We prove a general version of the stochastic Fubini theorem for stochastic integrals of Banach space valued processes with respect to compensated Poisson random measures under weak integrability assumptions, which extends this classical result from Hilbert space setting to Banach space setting.展开更多
基金supported by the Natural Science Foundation of China (No. 60874062)the Program for New Century Excellent Talents in University(No. NCET-10-0133)that in Heilongjiang Province (No.1154-NCET-01)
文摘This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random measurement delays. A new model that describes the random delays is constructed where possible the largest delay is bounded. Based on this new model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. A simulation example shows the effectiveness of the proposed algorithms.
基金Zhongkai Guo supported by NSF of China(Nos.11526196,11801575)the Fundamental Research Funds for the Central Universities,South-Central University for Nationalities(Grant Number:CZY20014)+1 种基金Hongbo Fu is supported by NSF of China(Nos.11826209,11301403)Natural Science Foundation of Hubei Province(No.2018CFB688).
文摘This article deals with an averaging principle for Caputo fractional stochastic differential equations with compensated Poisson random measure.The main contribution of this article is impose some new averaging conditions to deal with the averaging principle for Caputo fractional stochastic differential equations.Under these conditions,the solution to a Caputo fractional stochastic differential system can be approximated by that of a corresponding averaging equation in the sense ofmean square.
文摘Let D be a convolution semigroup of random measures or point processes on a locally compact second countable T 2space. There is a topological isomorphism from D into a subsemigroup of product topological semigroup (R +,+) N.D is a sequentially stable and D-separable ZH-semigroup, as well as a metrizable, stable and normable Hun semigroup, so it has the corresponding properties. In particular the author has a new and simple proof byZH-semigroup approach or Hun semigroup approach to show that D has property ILID (an infinitesimal array limit is infinitely divisible), and know the Baire types which some subsets of D belong in.
基金supported by National Natural Science Foundation of China(Grant Nos.11101222,11101223 and 11271203)the China Scholarship Council(CSC)(Grant No.201208120071)
文摘We study a stochastic Cahn-Hilliard equation driven by a Poisson random measure with Neumann boundary conditions. The global weak solution is established for the equation. Moreover, the existence of a Lyapunov function for the equation and an invariant measure associated with the transition semigroup are proved.
文摘Backward stochastic differential equations (BSDE) are discussed in many papers. However, in those papers, only Brownian motion and Poisson process are considered. In this paper, we consider BSDE driven by continuous local martingales and random measures.
基金partially supported by the National Natural Science Foundation of China(11871382,12071361)partially supported by the National Natural Science Foundation of China(11971361,11731012)。
文摘In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).
基金Supported by the NSF of the Higher Education Institutions of Jiangsu Province(10KJD110006)Supported by the grant of Jiangsu Institute of Education(Jsjy2009zd03)Supported by the Qing Lan Project of Jiangsu Province(2010)
文摘In this paper,we present the semi-implicit Euler(SIE)numerical solution for stochastic pantograph equations with jumps and prove that the SIE approximation solution converges to the exact solution in the mean-square sense under the Local Lipschitz condition.
基金Supported by the National Natural Science Foundation of China(11531013,U1630116)the fundamental research funds for the central universities.
文摘This paper provides a contemporary overview of phase retrieval problem with PhaseLift algorithm and summarizes theoretical results which have been derived during the past few years.Based on the lifting technique,the phase retrieval problem can be transformed into the low rank matrix recovery problem and then be solved by convex programming known as PhaseLift.Thus,stable guarantees for such problem have been gradually established for measurements sampled from sufficiently random distribution,for instance,the standard normal distribution.Further,exact recovery results have also been set up for masked Fourier measurements which are closely related to practical applications.
文摘The open set condition is the weakest condition hitherto in multifractal decomposition on the recursive sets. This paper deals with certain recursive fractals which have no relevence to the separation condition and gives their multifractal decomposition.
基金funded by a grant from the Natural Sciences and Engineering Research Council of Canada.
文摘In this article, we give a new proof of the Itôformula for some integral processes related to the space-time Lévy noise introduced in [1] [2] as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two applications of this result, which are useful in the study of SPDEs driven by a space-time Lévy noise with finite variance: a maximal inequality for the p-th moment of the stochastic integral, and the Itôrepresentation theorem leading to a chaos expansion similar to the Gaussian case.
基金supported by the National Basic Research Program of China (973 Program) under Grant No.2007CB814904the National Natural Science Foundations of China under Grant Nos.10921101 and 10701050the Natural Science Foundation of Shandong Province under Grant Nos.JQ200801 and 2008BS01024
文摘Both necessary and sufficient maximum principles for optimal control of stochastic systemwith random jumps consisting of forward and backward state variables are proved.The control variableis allowed to enter both diffusion and jump coefficients.The result is applied to a mean-varianceportfolio selection mixed with a recursive utility functional optimization problem.Explicit expressionof the optimal portfolio selection strategy is obtained in the state feedback form.
文摘The problem of reconstructing n-by-n structured matrix signal X=(x1,...,xn)via convex optimization is investigated,where each column xj is a vector of s-sparsity and all columns have the same l1-norm value.In this paper,the convex programming problem was solved with noise-free or noisy measurements.The uniform sufficient conditions were established which are very close to necessary conditions and non-uniform conditions were also discussed.In addition,stronger conditions were investigated to guarantee the reconstructed signal’s support stability,sign stability and approximation-error robustness.Moreover,with the convex geometric approach in random measurement setting,one of the critical ingredients in this contribution is to estimate the related widths’bounds in case of Gaussian and non-Gaussian distributions.These bounds were explicitly controlled by signal’s structural parameters r and s which determined matrix signal’s column-wise sparsity and l1-column-flatness respectively.This paper provides a relatively complete theory on column-wise sparse and l1-column-flat matrix signal reconstruction,as well as a heuristic foundation for dealing with more complicated high-order tensor signals in,e.g.,statistical big data analysis and related data-intensive applications.
基金supported by the National Natural Science Foundation of China(No.61101186)
文摘For maritime radiation source target tracking in particular electronic counter measures(ECM)environment,there exists two main problems which can deteriorate the tracking performance of traditional approaches.The frst problem is the poor observability of the radiation source.The second one is the measurement uncertainty which includes the uncertainty of the target appearing/disappearing and the detection uncertainty(false and missed detections).A novel approach is proposed in this paper for tracking maritime radiation source in the presence of measurement uncertainty.To solve the poor observability of maritime radiation source target,using the radiation source motion restriction,the observer altitude information is incorporated into the bearings-only tracking(BOT)method to obtain the unique target localization.Then the two uncertainties in the ECM environment are modeled by the random fnite set(RFS)theory and the Bernoulli fltering method with the observer altitude is adopted to solve the tracking problem of maritime radiation source in such context.Simulation experiments verify the validity of the proposed approach for tracking maritime radiation source,and also demonstrate the superiority of the method compared with the traditional integrated probabilistic data association(IPDA)method.The tracking performance under different conditions,particularly those involving different duration of radiation source opening and switching-off,indicates that the method to solve our problem is robust and effective.
基金supported by the National Natural Science Foundation of China under Grant Nos.60874032 and 70971079
文摘This paper discusses the H∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including internal stability and external stability, which enables to prove the bounded real lemma for the systems. By means of Riccati equations, infinite horizon linear stochastic state-feedback H∞ control design is also extended to such systems.
基金supported by the National Natural Science Foundation of China (Nos. 10771122,11071145)the Shandong Provincial Natural Science Foundation of China (No. Y2006A08)+2 种基金the Foundation for Innovative Research Groups of National Natural Science Foundation of China (No. 10921101)the National Basic Research Program of China (the 973 Program) (No. 2007CB814900)the Independent Innovation Foundation of Shandong University (No. 2010JQ010)
文摘Backward doubly stochastic differential equations driven by Brownian motions and Poisson process (BDSDEP) with non-Lipschitz coefficients on random time interval are studied. The probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations (SPDIEs) is treated with BDSDEP. Under non-Lipschitz conditions, the existence and uniqueness results for measurable solutions to BDSDEP are established via the smoothing technique. Then, the continuous depen- dence for solutions to BDSDEP is derived. Finally, the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given.
基金supported by the LPMC at Nankai University and National Natural Science Foundation of China(Grant No. 10671036)
文摘In this paper, we establish existence and uniqueness of the mild solutions to a class of neutral stochastic evolution equations driven by Poisson random measures in some Hilbert space. Moreover, we adopt the Faedo-Galerkin scheme to approximate the solutions.
基金supported by the National Natural Science Foundation of China under Grant Nos.11171187,11222110Shandong Province under Grant No.JQ201202+1 种基金Program for New Century Excellent Talents in University under Grant No.NCET-12-0331111 Project under Grant No.B12023
文摘This paper discusses mean-field backward stochastic differentiM equations (mean-field BS- DEs) with jumps and a new type of controlled mean-field BSDEs with jumps, namely mean-field BSDEs with jumps strongly coupled with the value function of the associated control problem. The authors first prove the existence and the uniqueness as well as a comparison theorem for the above two types of BSDEs. For this the authors use an approximation method. Then, with the help of the notion of stochastic backward semigroups introduced by Peng in 1997, the authors get the dynamic programming principle (DPP) for the value functions. Furthermore, the authors prove that the value function is a viscosity solution of the associated nonlocal Hamilton-Jacobi-Bellman (HJB) integro-partial differential equation, which is unique in an adequate space of continuous functions introduced by Barles, et al. in 1997.
基金supported by National Natural Science Foundation of China(Grant Nos.11571043,11431014 and 11871008)supported by National Natural Science Foundation of China(Grant Nos.11871382 and 11671076)
文摘For stochastic reaction-diffusion equations with Levy noises and non-Lipschitz reaction terms,we prove that W\H transportation cost inequalities hold for their invariant probability measures and for their process-level laws on the path space with respect to the L1-metrie.The proofs are based on the Galerkin approximations.
基金Supported by NNSFC(Grant Nos.11571147,11822106 and 11831014)NSF of Jiangsu Province(Grant No.BK20160004)the PAPD of Jiangsu Higher Education Institutions。
文摘We prove a general version of the stochastic Fubini theorem for stochastic integrals of Banach space valued processes with respect to compensated Poisson random measures under weak integrability assumptions, which extends this classical result from Hilbert space setting to Banach space setting.