非Lipschitz条件下的倒向重随机微分方程

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.     

A Type of General Forward-Backward Stochastic Differential Equations and Applications

The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with It?o’s stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations. The existence and uniqueness results of the general FBSDEs are obtained. In the framework of the general FBSDEs in this paper, the explicit form of the optimal control for linearquadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.     

Non-Linear Time-Advanced Backward Stochastic Partial Differential Equations With Jumps

We prove an existence and uniqueness result for non-linear time-advanced backward stochastic partial differential equations with jumps (ABSPDEJs). We then apply our results to study a time-advanced backward type of stochastic generalized porous medium equations with jumps.     

Strong Solutions of Semilinear Parabolic Equations with Measure Data and Generalized Backward Stochastic Differential Equations

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.     

正倒向随机微分方程理论及应用

正倒向随机微分方程源于随机控制和金融等问题的研究,反之,方程理论的研究成果在控制、金融等领域也有着重要的应用。基于正向和倒向随机微分方程的理论成果,正倒向随机微分方程的研究在短时间内取得了长足进步。本文将从方程可解性这一角度出发,对正倒向随机微分方程目前取得的成果进行系统的总结与探讨。     

The Link between Stochastic Differential Equations with Non-Markovian Coefficients and Backward Stochastic Partial Differential Equations

In this paper, we conjecture and prove the link between stochastic differential equations with non-Markovian coefficients and nonlinear parabolic backward stochastic partial differential equations, which is an extension of such kind of link in Markovian framework to non-Markovian framework.Different from Markovian framework, where the corresponding partial differential equation is deterministic, the backward stochastic partial differential equation here has a pair of adapted solutions, and thus the link has a much different form. Moreover, two examples are given to demonstrate the applications of the derived link.     

Kolmogorov向前向后方程组的概率意义

研究了Kolmogorov向前向后方程组的概率意义,得到正规链满足Kolmogorov向前向后方程组的等价条件,并进一步得到不诚实但全稳定的转移函数对应的带“杀死”的Markov链满足Kolmogorov向前向后方程组的充分必要条件.     

系数为左Lipschitz的倒向随机微分方程解的存在性

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.     

具有非Lipschitz和非增长条件的带跳倒向随机微分方程

本文研究一类带Poisson跳的倒向随机微分方程。在方程的系数满足非增长条件和非Lipschitz条件下,讨论方程适应解的存在唯一性和稳定性。为了证明解的存在性,首先通过函数变换,构造出一逼近序列,然后运用推广的Bihari不等式和Lebesgue控制收敛定理证明该逼近序列是收敛的,得到逼近序列的极限就是方程的适应解。解的唯一性和稳定性主要运用了Bihari不等式和推广的Bihari不等式来进行证明。     

BSDEs with Jumps and Path-Dependent Parabolic Integro-differential Equations

This paper deals with backward stochastic differential equations with jumps, whose data (the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential equations, and then obtains a new type of nonlinear Feynman-Kac formula related to such BSDEs with jumps under some regularity conditions.     

Some Results on Nonlinear Backward Stochastic Evolution Equations

Abstract

In this paper, we present some results concerning existence and uniqueness of solutions for a rather general class of nonlinear backward stochastic partial differential equations. These results are illustrated with two examples.     

无界停时终端非李氏系数带跳倒向随机微分方程的解及拟线性椭圆型偏微分积分方程解的概率表示

对终端为无界停时的带跳倒向随机微分方程,在非李氏条件下证得了解的存在唯一性.推导出这类方程解的若干收敛定理与解对参数的连续依赖性,还得到了关于拟线性随圆型偏微分积分方程解的概率表示.     

关于反射倒向随机微分方程的解的一些性质(英文)

研究了关于反射倒向随机微分方程的解的一些性质.同时在适当的条件下建立了关于反射倒向随机微分方程生成元的一个唯一性定理和一个逆比较定理.     

关于反射倒向随机微分方程的解的一些性质

研究了关于反射倒向随机微分方程的解的一些性质．同时在适当的条件下建立了关于反射倒向随机微分方程生成元的一个唯一性定理和一个逆比较定理．     

A Stabilized Galerkin Scheme for the Convection-Diffusion-Reaction Equations

A fully discrete stabilized scheme is proposed for solving the time-dependent convection-diffusion-reaction equations. A time derivative term results in our stabilized algorithm. The finite element method for spatial discretization and the backward Euler or Crank-Nicolson scheme for time discretization are employed. The long-time stability and convergence are established in this article. Finally, some numerical experiments are provided to confirm the theoretical analysis.     

��Levy���������ķ����͵������΢�ַ���

??In this paper, we prove the existence and uniqueness of solutions for reflected backward stochastic differential equations driven by a Levy process, in which the reflecting barriers are just right continuous with left limits whose jumps are arbitrary. To derive the above results, the monotonic limit theorem of Backward SDE associated with Levy process is established.     

Stability Analysis of Modified Multilag Methods for Volterra Integral Equations

Stability analysis of modified multilag methods for Volterraintegral equations of the second and first kind is presented,based respectively on the test equations This analysis reinforces the opinion that modified multilagmethods are advantageous over quadrature methods for Volterraequations. They allow us to combine the good stability propertiesof backward differentiation formulae and the efficiency of Adams-Moultonformulae for ordinary differential equations.     

General Full Implicit Strong Taylor Approximations for Stiff Stochastic Differential Equations

In this paper, we present the backward stochastic Taylor expansions for a Ito process, including backward Ito-Taylor expansions and backward Stratonovich-Taylor expansions. We construct the general full implicit strong Taylor approximations (including Ito-Taylor and Stratonovich-Taylor schemes) with implicitness in both the deterministic and the stochastic terms for the stiff stochastic differential equations (SSDE) by employing truncations of backward stochastic Taylor expansions. We demonstrate that these schemes will converge strongly with corresponding order $1,2,3,\ldots$ Mean-square stability has been investigated for full implicit strong Stratonovich-Taylor scheme with order $2$, and it has larger mean-square stability region than the explicit and the semi-implicit strong Stratonovich-Taylor schemes with order $2$. We can improve the stability of simulations considerably without too much additional computational effort by using our full implicit schemes. The full implicit strong Taylor schemes allow a larger range of time step sizes than other schemes and are suitable for SSDE with stiffness on both the drift and the diffusion terms. Our numerical experiment shows these points.     

Backward Stochastic Differential Equations for a Single Jump Process

We consider backward stochastic differential equations (BSDEs) related to a finite continuous time single jump process. We prove the existence and uniqueness of solutions when the coefficients satisfy Lipschitz continuity conditions. A comparison theorem for these solutions is also given. Applications to the theory of nonlinear expectations are then investigated.