带随机跳跃的线性二次非零和微分对策问题

对于一类以布朗运动和泊松过程为噪声源的正倒向随机微分方程,在单调性假设下,给出了解的存在性和唯一性的结果．然后将这些结果应用于带随机跳跃的线性二次非零和微分对策问题之中,由上述正倒向随机微分方程的解得到了开环Nash均衡点的显式形式．     

带跳和右连左极障碍的反射非Lipschitz倒向随机微分方程(英文）

本文考虑一类由布朗运动和泊松点过程驱动的非Lipschitz系数的一维倒向随机微分方程,并要求它的解在一右连左极的障碍过程的上方.利用罚方法和迭代方法证得该类方程解的存在唯一性.     

由Levy过程驱动的倒向随机微分方程在局部Bihari条件下解的存在唯一性

本文利用推广的Bihari不等式和截断函数,证明了由Levy过程驱动的倒向随机微分方程在局部Bihari条件下解的存在唯一性。我们先给出在某种较弱的条件下,方程在局部区间[T0,T],明上解的存在唯一性,然后加强条件,得到解的全局存在唯一性,从而推广了周和秦的结论。     

分数布朗运动驱动下z一致连续的BSDE解的存在性与唯一性

本文研究一类由分数布朗运动驱动的一维倒向随机微分方程解的存在性与唯一性问题,在假设其生成元满足关于y Lipschitz连续,但关于z一致连续的条件下,通过应用分数布朗运动的Tanaka公式以及拟条件期望在一定条件下满足的单调性质,得到倒向随机微分方程的解的一个不等式估计,应用Gronwall不等式得到了一个关于这类方程的解的存在性与唯一性结果,推广了一些经典结果以及生成元满足一致Lipschitz条件下的由分数布朗运动驱动的倒向随机微分方程解的结果.     

由Lévy过程驱动的倒向随机微分方程在局部Bihari条件下解的存在唯一性

本文利用推广的Bihari不等式和截断函数,证明了由Lévy过程驱动的倒向随机微分方程在局部Bihari条件下解的存在唯一性。我们先给出在某种较弱的条件下,方程在局部区间[T0,T]上解的存在唯一性,然后加强条件,得到解的全局存在唯一性,从而推广了周和秦的结论。     

一类非Lipschitz条件的Backward SDE适应解的存在唯一性

本文中，我们在非Lipschitz条件下证明了倒向随机微分方程的局部与整体适应解的存在唯一性，推广了PaLrdoux-Peng定理．     

由Levy过程驱动的倒向随机微分方程在随机单调条件下解的存在唯一性

本文讨论了如下的由Levy过程驱动的倒向随机微分方程适应解的存在唯一性■其中W_s是一Wiener过程,H_s为由Levy过程构成Teugels鞅.我们通过构造函数逼近序列的方法证明了,在漂移系数f关于Y满足随机单调,f关于Z和U满足随机Lipschitz条件下,方程存在唯一适应解.     

定价问题和一类倒向随机微分方程解的存在唯一性

本文建立了由一个多维Brown运动、Poisson过程和跳时固定的简单点过程共同驱动的股票价格模型．在此模型下，将未定权益的定价问题归结为一类倒向随机微分方程的求解问题．证明了这类倒向随机微分方程适应解的存在唯一性问题，并给出了一个关于未定权益的定价公式．     

广义Khasminskii条件下自变量分段连续型带Poisson随机测度随机微分方程Euler方法的依概率收敛性

针对满足广义Khasminskii条件的由维纳过程和泊松随机测度驱动的自变量分段连续型随机微分方程(EPCASDEs),给出了Euler方法,广义Khasminskii条件比经典条件包容了更多的EPC.ASDEs.现有文献对该类方程的研究成果较少.针对EPCASDEs在广义Khasminskii条件下证明了全局解的存在唯一性,并研究了Euler方法的依概率收敛性.给出了数值算例支持主要结论.     

非Lipschitz条件下的包含下微分算子的带跳倒向随机微分方程(英文)

本文在非Lipschitz系数下,考虑了一类多值的倒向随机微分方程.利用极大单调算子的Yosida估计和倒向随机微分方程在非Lipschitz条件下解的存在唯一性,获得了多值带跳的倒向随机微分方存在唯一解的结论.     

BSDEs with two RCLL reflecting obstacles driven by Brownian motion and Poisson measure and a related mixed zero-sum game

In this paper we study Backward Stochastic Differential Equations with two reflecting right continuous with left limit obstacles (or barriers) when the noise is given by Brownian motion and a mutually independent Poisson random measure. The jumps of the obstacle processes could be either predictable or inaccessible. We show the existence and uniqueness of the solution when the barriers are completely separated and the generator uniformly Lipschitz. We do not assume the existence of a difference of supermartingales between the obstacles. As an application, we show that the related mixed zero-sum differential–integral game problem has a value.     

Regularity of strong solutions of one-dimensional SDE’s with discontinuous and unbounded drift

In this paper we develop a method for constructing strong solutions of one-dimensional Stochastic Differential Equations where the drift may be discontinuous and unbounded. The driving noise is the Brownian Motion and we show that the solution is Sobolev-differentiable in the initial condition and Malliavin differentiable. This method is not based on a pathwise uniqueness argument. We will apply these results to the stochastic transport equation. More specifically, we obtain a continuously differentiable solution of the stochastic transport equation when the driving function is a step function.     

Backward SDEs with two rcll reflecting barriers without Mokobodski's hypothesis

In this paper we study Backward Stochastic Differential Equations with two reflecting right continuous with left limits (rcll) barriers. We show existence and uniqueness of the solution when the barriers are completely separated and the generator is uniformly Lipschitz.     

One barrier reflected backward doubly stochastic differential equations with continuous generator

We prove the existence and uniqueness of solutions to Reflected Backward Doubly Stochastic Differential Equations (RBDSDEs) with one continuous barrier and uniformly Lipschitz coefficients. The existence of a maximal and a minimal solution for RBDSDEs with continuous generator is also established. To cite this article: K. Bahlali et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

A class of stochastic differential equations with the time average

Stochastic diferential equations with the time average have received increasing attentions in recent years since they can ofer better explanations for some fnancial models.Since the time average is involved in this class of stochastic diferential equations,in this paper,the linear growth condition and the Lipschitz condition are diferent from the classical conditions.Under the special linear growth condition and the special Lipschitz condition,this paper establishes the existence and uniqueness of the solution.By using the Lyapunov function,this paper also establishes the existence and uniqueness under the local Lipschitz condition and gives the p-th moment estimate.Finally,a scalar example is given to illustrate the applications of our results.     

A Class of Stochastic Diferential Equations with the Time Average

Stochastic diferential equations with the time average have received increasing attentions in recent years since they can ofer better explanations for some fnancial models.Since the time average is involved in this class of stochastic diferential equations,in this paper,the linear growth condition and the Lipschitz condition are diferent from the classical conditions.Under the special linear growth condition and the special Lipschitz condition,this paper establishes the existence and uniqueness of the solution.By using the Lyapunov function,this paper also establishes the existence and uniqueness under the local Lipschitz condition and gives the p-th moment estimate.Finally,a scalar example is given to illustrate the applications of our results.     

Time inhomogeneous Stochastic Differential Equations involving the local time of the unknown process,and associated parabolic operators

In this paper we study time inhomogeneous versions of one-dimensional Stochastic Differential Equations (SDE) involving the Local Time of the unknown process on curves. After proving existence and uniqueness for these SDEs under mild assumptions, we explore their link with Parabolic Differential Equations (PDE) with transmission conditions. We study the regularity of solutions of such PDEs and ensure the validity of a Feynman–Kac representation formula. These results are then used to characterize the solutions of these SDEs as time inhomogeneous Markov Feller processes.     

随机游走和离散的倒向随机微分方程

本文研究了随机游走和离散的倒向随机微分方程。把随机游走到布朗运动的收敛推广到L^2情形；而且根据倒向随机微分方程的理论框架研究了离散的倒向随机微分方程，得到了离散的倒向随机微分方程解的存在唯一性和比较定理，这实际上给出了倒向随机微分方程的一种离散方法，为理论和实际研究提供了方便。     

Reflected Backward Stochastic Differential Equation with Locally Monotone Coefficient

Abstract

We study the existence and uniqueness of Reflected Backward Stochastic Differential Equation (RBSDE for short) with both monotone and locally monotone coefficient and squared integrable terminal data. This is done with a polynomial growth condition on the coefficient. An application to the homogenization of multivalued Partial Differential Equations (PDEs for short) is given.     

Weak and strong solutions of Generalized Itô's Stochastic Functional Differential Equations

The fundamental theory of Generalized Itô's Stochastic Functional Differential Equations (GISFDE), namely, stochastic functional differential equations associated with a stochastic integral based onC-semimartingales, is discussed. The main purpose is to establish the concepts of GISFDE, weak solution, strong solution, solution-measure and several kinds of the uniqueness of solution, to show the relationships smong these solutions and get existence and uniqueness theorems of the solution.