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
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
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
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
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
The analysis of the filamentary structure of the cosmo as well as that of the internal structure of the polar ice suggests the development of models based on three-dimensional(3D)point processes.A point process,regard...The analysis of the filamentary structure of the cosmo as well as that of the internal structure of the polar ice suggests the development of models based on three-dimensional(3D)point processes.A point process,regarded as a random measure,can be expressed as a sum of Delta Dirac measures concentrated at some random points.The integration with respect to the point process leads the continuous wavelet transform of the process itself.As possible mother wavelets,we propose the application of the Mexican hat and the Morlet wavelet in order to implement the scale-angle energy density of the process,depending on the dilation parameter and on the three angles which define the direction in the Euclidean space.Such indicator proves to be a sensitive detector of any variation in the direction and it can be successfully implemented to study the isotropy or the filamentary structure in 3D point patterns.展开更多
Using the weak convergence method introduced by A.Budhiraja,P.Dupuis,and A.Ganguly[Ann.Probab.,2016,44:1723-1775],we establish the moderate deviation principle for neutral functional stochastic differential equations ...Using the weak convergence method introduced by A.Budhiraja,P.Dupuis,and A.Ganguly[Ann.Probab.,2016,44:1723-1775],we establish the moderate deviation principle for neutral functional stochastic differential equations driven by both Brownian motions and Poisson random measures.展开更多
Existence and uniqueness results of the solution to fully coupled forward-backward stochastic defferential equations with Brownian motion and Poisson process are obtained. Many stochastic Hamilton systems arising in s...Existence and uniqueness results of the solution to fully coupled forward-backward stochastic defferential equations with Brownian motion and Poisson process are obtained. Many stochastic Hamilton systems arising in stochastic optimal control systems with random jump and in mathemstical finance with security price discontinuously changing can be treated with these results. The continuity of the solution depending on parameters is also proved in this paper.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 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.
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 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.
文摘The analysis of the filamentary structure of the cosmo as well as that of the internal structure of the polar ice suggests the development of models based on three-dimensional(3D)point processes.A point process,regarded as a random measure,can be expressed as a sum of Delta Dirac measures concentrated at some random points.The integration with respect to the point process leads the continuous wavelet transform of the process itself.As possible mother wavelets,we propose the application of the Mexican hat and the Morlet wavelet in order to implement the scale-angle energy density of the process,depending on the dilation parameter and on the three angles which define the direction in the Euclidean space.Such indicator proves to be a sensitive detector of any variation in the direction and it can be successfully implemented to study the isotropy or the filamentary structure in 3D point patterns.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11671034,11771327,61703001).
文摘Using the weak convergence method introduced by A.Budhiraja,P.Dupuis,and A.Ganguly[Ann.Probab.,2016,44:1723-1775],we establish the moderate deviation principle for neutral functional stochastic differential equations driven by both Brownian motions and Poisson random measures.
文摘Existence and uniqueness results of the solution to fully coupled forward-backward stochastic defferential equations with Brownian motion and Poisson process are obtained. Many stochastic Hamilton systems arising in stochastic optimal control systems with random jump and in mathemstical finance with security price discontinuously changing can be treated with these results. The continuity of the solution depending on parameters is also proved in this paper.