By using the Mecke identity, we study a class of birth-death type Dirichlet forms associated with the mixed Poisson measure. Both Poincare and weak Poincare inequalities are established, while another Poincare type in...By using the Mecke identity, we study a class of birth-death type Dirichlet forms associated with the mixed Poisson measure. Both Poincare and weak Poincare inequalities are established, while another Poincare type inequality is disproved under some reasonable assumptions.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
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
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
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 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
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
Kerov[16,17] proved that Wigner's semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under t...Kerov[16,17] proved that Wigner's semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov's partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.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
Let L be a Schrdinger operator of the form L =-? + V acting on L^2(R^n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R^n) denote the BMO space associated to ...Let L be a Schrdinger operator of the form L =-? + V acting on L^2(R^n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R^n) denote the BMO space associated to the Schrdinger operator L on R^n. In this article, we show that for every f ∈ BMO_L(R^n) with compact support, then there exist g ∈ L~∞(R^n) and a finite Carleson measure μ such that f(x) = g(x) + S_(μ,P)(x) with ∥g∥∞ + |||μ|||c≤ C∥f∥BMO_L(R^n), where S_(μ,P)=∫(R_+^(n+1))Pt(x,y)dμ(y, t),and Pt(x, y) is the kernel of the Poisson semigroup {e-^(t(L)^(1/2))}t>0 on L^2(R^n). Conversely, if μ is a Carleson measure, then S_(μ,P) belongs to the space BMO_L(R^n). This extends the result for the classical John-Nirenberg BMO space by Carleson(1976)(see also Garnett and Jones(1982), Uchiyama(1980) and Wilson(1988)) to the BMO setting associated to Schrdinger operators.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
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
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
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
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
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130141120036)the International Postdoctoral Exchange Fellowship Program(2013)the Fundamental Research Funds for the Central Universities
文摘By using the Mecke identity, we study a class of birth-death type Dirichlet forms associated with the mixed Poisson measure. Both Poincare and weak Poincare inequalities are established, while another Poincare type inequality is disproved under some reasonable assumptions.
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.
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 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.
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 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(No.10671176)
文摘Kerov[16,17] proved that Wigner's semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov's partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.
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.
基金supported by National Natural Science Foundation of China (Grant Nos. 11501583, 11471338, 11622113, 11371378 and 11521101)Australian Research Council Discovery (Grant Nos. DP 140100649 and DP 170101060)+1 种基金Guangdong Natural Science Funds for Distinguished Young Scholar (Grant No. 2016A030306040)Guangdong Special Support Program
文摘Let L be a Schrdinger operator of the form L =-? + V acting on L^2(R^n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R^n) denote the BMO space associated to the Schrdinger operator L on R^n. In this article, we show that for every f ∈ BMO_L(R^n) with compact support, then there exist g ∈ L~∞(R^n) and a finite Carleson measure μ such that f(x) = g(x) + S_(μ,P)(x) with ∥g∥∞ + |||μ|||c≤ C∥f∥BMO_L(R^n), where S_(μ,P)=∫(R_+^(n+1))Pt(x,y)dμ(y, t),and Pt(x, y) is the kernel of the Poisson semigroup {e-^(t(L)^(1/2))}t>0 on L^2(R^n). Conversely, if μ is a Carleson measure, then S_(μ,P) belongs to the space BMO_L(R^n). This extends the result for the classical John-Nirenberg BMO space by Carleson(1976)(see also Garnett and Jones(1982), Uchiyama(1980) and Wilson(1988)) to the BMO setting associated to Schrdinger operators.
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.
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 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 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.
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.