共查询到20条相似文献,搜索用时 15 毫秒
1.
2003年Briand et al等在很一般的假设下建立了倒向随机微分方程(BSDEs)L^p解的存在唯一性定理.本文在此基础上得到了这种假设下一维BSDEs的L^p解的几个连续性质. 相似文献
2.
Backward doubly stochastic differential equations driven by Brownian motions and Poisson process(BDSDEP) with non-Lipschitz coeffcients 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 dependence for solutions to BDSDEP is derived.Finally,the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given. 相似文献
3.
We give the probabilistic interpretation of the solutions in Sobolev spaces of parabolic semilinear stochastic PDEs in terms of Backward Doubly Stochastic Differential Equations. This is a generalization of the Feynman–Kac formula. We also discuss linear stochastic PDEs in which the terminal value and the coefficients are distributions. 相似文献
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The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation
with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov equation and to stochastic
optimal control. 相似文献
5.
研究了平均场倒向随重机微分方程,得到了平均场倒向重随机微分方程解的存在唯一性.基于平均场倒向重随机微分方程的解,给出了一类非局部随机偏微分方程解的概率解释.讨论了平均场倒向重随机系统的最优控制问题,建立了庞特利亚金型的最大值原理.最后讨论了一个平均场倒向重随机线性二次最优控制问题,展示了上述最大值原理的应用. 相似文献
6.
Tomasz Klimsiak 《Potential Analysis》2012,36(2):373-404
We prove that under natural assumptions on the data strong solutions in Sobolev spaces of semilinear parabolic equations in
divergence form involving measure on the right-hand side may be represented by solutions of some generalized backward stochastic
differential equations. As an application we provide stochastic representation of strong solutions of the obstacle problem
by means of solutions of some reflected backward stochastic differential equations. To prove the latter result we use a stochastic
homographic approximation for solutions of the reflected backward equation. The approximation may be viewed as a stochastic
analogue of the homographic approximation for solutions to the obstacle problem. 相似文献
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Shaokuan Chen 《随机分析与应用》2013,31(5):820-841
In this article, we study one-dimensional backward stochastic differential equations with continuous coefficients. We show that if the generator f is uniformly continuous in (y, z), uniformly with respect to (t, ω), and if the terminal value ξ ∈L p (Ω, ? T , P) with 1 < p ≤ 2, the backward stochastic differential equation has a unique L p solution. 相似文献
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倒向随机微分方程由Pardoux和彭实戈首先提出,彭实戈给出了一维BSDE的比较定理,周海滨将其推广到了高维情形.毛学荣将倒向随机微分方程解的存在唯一性定理推广到非Lipschitz系数情况,曹志刚和严加安给了相应的一维比较定理.本文将曹志刚和严加安的比较定理推广到高维情形. 相似文献
11.
This paper is devoted to study backward stochastic differential equations in the plane driven by a Brownian sheet, where the value of the solution at the corner (s
0,t
0) is fixed. The existence and uniqueness of a solution is obtained by means of Picard's approximation scheme and a suitable two-parameter Gronwall's type lemma. 相似文献
12.
贾广岩 《数学年刊A辑(中文版)》2007,(5)
考虑一类一维倒向随机微分方程(BSDE),其系数关于y满足左Lipschitz条件(可能是不连续的),关于z满足Lipschitz条件.在这样的条件下,证明了BSDE的解是存在的,并且得到了相应的比较定理. 相似文献
13.
Long JIANG Department of Mathematics China University of Mining Technology Xuzhou Jiangsu China School of Mathematical Sciences Fudan University Shanghai China School of Mathematics System Sciences Shandong University Jinan China. 《数学年刊B辑(英文版)》2006,27(5)
Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen's inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g(t, 0) = 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen's inequality for g-expectation in [4, 7-9]. 相似文献
14.
该文研究了非Lipschitz条件下的倒向重随机微分方程, 给出了此类方程解的存在唯一性 定理, 推广Pardoux和Peng 1994年的结论; 同时也得到了此类方程在非Lipschitz条件下的比较定理, 推广了Shi,Gu和Liu 2005年的结果. 从而推广倒向重随机微分方程在随机控制和随机偏微分方程在 粘性解方面的应用. 相似文献
15.
Existence and uniqueness theorems for parabolic stochastic partial differential equations with space—time white noise are
proved. The method is a combination of the characterization theorem for Hida distributions with the Feynman—Kac and Girsanov
formulae.
Accepted 3 December 1996 相似文献
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Qiang Han & Shaolin Ji 《计算数学(英文版)》2023,41(2):287-304
In this paper, a stochastic linear two-step scheme has been presented to approximate backward stochastic differential equations (BSDEs). A necessary and sufficient condition is given to judge the $\mathbb{L}_2$-stability of our numerical schemes. This stochastic linear two-step method possesses a family of $3$-order convergence schemes in the sense of strong stability. The coefficients in the numerical methods are inferred based on the constraints of strong stability and $n$-order accuracy ($n\in\mathbb{N}^+$). Numerical experiments illustrate that the scheme is an efficient probabilistic numerical method. 相似文献
18.
We investigate the approximation by space and time discretization of quasi linear evolution equations driven by nuclear or space time white noise. An error bound for the implicit Euler, the explicit Euler, and the Crank–Nicholson scheme is given and the stability of the schemes are considered. Lastly we give some examples of different space approximation, i.e., we consider approximation by eigenfunction, finite differences and wavelets. 相似文献
19.
In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedback regulator for the optimal control problem by using the solutions of a group of Riccati equations. 相似文献