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1.
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
2.
在生成元~$g$~的第~$i$~个分量~$g_i(t,y,z)$~仅仅依赖于矩阵~$z$~的第~$i$
行的条件下, Hamad\`{e}ne于2003年证明了生成元一致连续的倒向随机微分
方程的~$L^2$~解的存在性, 其~$L^2$~解的唯一性由范胜君等于2010年得到. 本文进一步地证明了该类倒向随机微分
方程的~$L^p\ (p>1)$~解的存在唯一性. 相似文献
3.
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
4.
We study a forward-backward system
of stochastic differential equations in an
infinite-dimensional framework and its relationships
with a semilinear parabolic differential equation on a Hilbert space,
in the spirit of the approach of Pardoux-Peng.
We prove that the stochastic system
allows us to construct a unique
solution of the parabolic equation in
a suitable class of locally Lipschitz real
functions. The parabolic equation is understood in
a mild sense which requires the notion
of a generalized directional gradient, that
we introduce by a probabilistic approach
and prove to exist for locally Lipschitz
functions.
The use of the generalized directional gradient
allows us to cover various applications to option
pricing problems and to optimal stochastic control problems
(including control of delay equations and
reaction--diffusion equations),
where the lack of differentiability of the coefficients
precludes differentiability of solutions to the associated
parabolic equations of Black--Scholes or Hamilton-Jacobi-Bellman
type. 相似文献
5.
6.
Coquet等人在g(t,y ,0 )≡ 0的条件下建立了一个关于倒向随机微分方程生成元g的逆比较定理 .本文对一般的倒向随机微分方程的生成元以及对L2 有界的生成元分别得到了两个新的逆比较定理 . 相似文献
7.
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
8.
本文建立了关于局部L2-有界的倒向随机微分方程生成元的表示定理,此定理推广了Co-quet等人的一个结果.应用该定理,本文给出了倒向随机微分方程的生成元是凹生成元的一个充分必要条件. 相似文献
9.
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
10.
11.
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
12.
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
13.
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
14.
15.
This paper is concerned with nonlinear partial differential equations of the calculus of variation (see [13]) perturbed
by noise. Well-posedness of the problem was proved by Pardoux in the seventies (see [14]), using monotonicity methods.
The aim of the present work is to investigate the asymptotic behaviour of the corresponding transition semigroup Pt. We show existence and, under suitable assumptions, uniqueness of an ergodic invariant measure ν. Moreover, we solve the
Kolmogorov equation and prove the so-called "identite du carre du champs". This will be used to study the Sobolev space W1,2(H,ν) and to obtain information
on the domain of the infinitesimal generator of Pt. 相似文献
16.
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
17.
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
18.
将倒向随机微分方程看作金融市场中的一个定价机制,而该机制具体体现就是生成元g.本文通过经典的Black-Scholes模型探讨了生成元g的经济含义,首次提出了生成元g的表达式中含有折现的概念,同时详细分析并说明了不同的生成元g可以反应同一未定权益价格过程的不同形态.最后结合上面的讨论给出了关于一定形式的生成元g的类Jensen不等式性质. 相似文献
19.
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