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Poincar and Weak Poincar Inequalities for the Mixed Poisson Measure
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作者 Chang Song DENG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第10期1719-1728,共10页
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
关键词 Mixed poisson measure Poincare inequality configuration space birth-death process
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An Averaging Principle for Caputo Fractional Stochastic Differential Equations with Compensated Poisson Random Measure 被引量:1
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作者 GUO Zhongkai FU Hongbo WANG Wenya 《Journal of Partial Differential Equations》 CSCD 2022年第1期1-10,共10页
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
关键词 Stochastic fractional differential equations averaging principle compensated poisson random measure
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The Semi-implicit Euler Method for Stochastic Pantograph Equations with Jumps 被引量:1
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作者 MAO Wei HAN Xiu-jing CHEN Bo 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第3期405-409,共5页
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
关键词 stochastic pantograph equations poisson random measure semi-implicit Euler method strong convergence
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Stochastic Cahn-Hilliard equations driven by Poisson random measures
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作者 JIANG YiMing SHI KeHua WANG SuXin 《Science China Mathematics》 SCIE 2014年第12期2563-2576,共14页
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
关键词 Cahn-Hilliard equations poisson random measures Lyapunov function invariant measure
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A LARGE DEVIATION PRINCIPLE FOR THE STOCHASTIC GENERALIZED GINZBURG-LANDAU EQUATION DRIVEN BY JUMP NOISE
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作者 王冉 张贝贝 《Acta Mathematica Scientia》 SCIE CSCD 2023年第2期505-530,共26页
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
关键词 large deviation principle weak convergence method stochastic generalized Ginzburg-Landau equation poisson random measure
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Ito Formula for Integral Processes Related to Space-Time Levy Noise
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作者 Raluca M.Balan Cheikh B.Ndongo 《Applied Mathematics》 2015年第10期1755-1768,共14页
In this article, we give a new proof of the It&ocirc;formula 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 It&ocirc;formula 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 It&ocirc;representation theorem leading to a chaos expansion similar to the Gaussian case. 展开更多
关键词 Levy Processes poisson Random measure Stochastic Integral Ito Formula Ito Representation Theorem
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H_∞ CONTROL FOR STOCHASTIC SYSTEMS WITH POISSON JUMPS 被引量:4
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作者 Xiangyun LIN Rui ZHANG 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2011年第4期683-700,共18页
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
关键词 Externally stable H∞ control internally stable poisson random measure Riccati equa-tion stochastic system with jumps.
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Transition Distributions of Young Diagrams Under Periodically Weighted Plancherel Measures
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作者 Zhong-gen Su 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2009年第4期655-674,共20页
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
关键词 Limit shape Limiting density of eigenvalues poissonized Plancherel measures in a periodic potential Transition distributions Unitary invariant matrix models
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FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH BROWNIAN MOTION AND POISSON PROCESS 被引量:14
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作者 吴臻 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1999年第4期433-443,共11页
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
关键词 Stochastic differential equations stochastic analysis random measure poisson process
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Carleson measures, BMO spaces and balayages associated to Schrdinger operators
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作者 CHEN Peng DUONG XuanThinh +2 位作者 LI Ji SONG Liang YAN LiXin 《Science China Mathematics》 SCIE CSCD 2017年第11期2077-2092,共16页
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
关键词 BMO space Carleson measure balayage poisson semigroup the reverse Holder class Schrodinger operators
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MAXIMUM PRINCIPLE FOR FORWARD-BACKWARD STOCHASTIC CONTROL SYSTEM WITH RANDOM JUMPS AND APPLICATIONS TO FINANCE 被引量:13
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作者 Jingtao SHI·Zhen WU School of Mathematics,Shandong University,Jinan 250100,China. 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2010年第2期219-231,共13页
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
关键词 Forward-backward stochastic control system maximum principle poisson random measure recursive utility stochastic optimal control.
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Controlled Mean-Field Backward Stochastic Differential Equations with Jumps Involving the Value Function 被引量:2
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作者 LI Juan MIN Hui 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2016年第5期1238-1268,共31页
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
关键词 Dynamic programming principle (DPP) Hamilton-Jacobi-Bellman (HJB) equation mean-field backward stochastic differential equation (mean-field BSDE) with jump poisson random measure value function.
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Approximating solutions of neutral stochastic evolution equations with jumps 被引量:1
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作者 BO LiJun SHI KeHua WANG YongJin 《Science China Mathematics》 SCIE 2009年第5期895-907,共13页
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
关键词 neutral stochastic evolution equations poisson random measures Faedo-Galerkin approximation 34A45 60H15
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Transportation Cost Inequalities for Stochastic Reaction-Diffusion Equations with Lévy Noises and Non-Lipschitz Reaction Terms 被引量:1
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作者 Yu Tao MA Ran WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2020年第2期121-136,共16页
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
关键词 Stochastic reaction-diffusion equation poisson random measure transportation cost in-equality
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Stochastic Fubini Theorem for Jump Noises in Banach Spaces
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作者 Jia Hui ZHU Wei LIU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2021年第3期423-435,共13页
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
关键词 Stochastic Fubini theorem martingale type p Banach space poisson random measure stochastic integration
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Moderate deviations for neutral functional stochastic differential equations driven by Levy noises
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作者 Xiaocui MA Fubao XI Dezhi LIU 《Frontiers of Mathematics in China》 SCIE CSCD 2020年第3期529-554,共26页
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
关键词 Moderate deviations neutral functional stochastic dierential equations poisson random measure
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