正倒向随机微分方程解的比较定理

讨论了正倒向随机微分方程解的比较问题.阐述了正倒向随机微分方程在随机最优控制、现代金融理论中的广泛而深刻的应用, 对于一类正倒向随机微分方程, 利用Ito公式、停时等随机分析方法,通过构造辅助正倒向随机微分方程,得到了正倒向随机微分方程解的比较定理.     

一类非时齐非Lipschitz条件下带跳的倒向随机微分方程的适应解及比较定理

对系数f(t,y,z,k)满足非常一般的非时齐非Lipschitz条件,本文给出一类带跳的倒向随机微分方程局部和整体解的存在唯一性的证明,同时本文也研究了带跳的倒向随机微分方程的比较定理,从而把前人的相应结果推广到更一般情形．     

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。     

反射倒向随机微分方程的逆比较问题(Ⅰ)

在Briand,Coquet,Hu,Memin,Peng[1],Coquet,Hu,Memin,Peng[2],Chen[3],Jiang [8]等中,研究了倒向随机微分方程的逆比较定理,就是通过比较倒向随机微分方程的解来比较倒向随机微分方程的生成元问题．在文[9]中Li和Tang首次研究了反射倒向随机微分方程的逆比较问题．本文考虑在更一般的条件下,反射倒向随机微分方程的生成元的逆比较问题．     

正倒向随机微分方程的适应解及其比较定理(英文)

研究了一类正倒向随机微分方程的适应解 ,其中正向方程不需要满足非退化条件 .我们证明了在某些单调条件下 ,正倒向随机微分方程存在唯一的适应解 ,并给出了该正倒向随机微分方程的比较定理 .     

由连续半鞅驱动的倒向随机微分方程解的比较定理

彭实戈[1]首先建立了一维倒向随机微分方程的比较定理,本文在Lipschitz条件下研究由连续半鞅驱动的倒向随机微分方程,我们将比较定理推广到此类倒向随机微分方程,并且证明方法比彭实戈[1]的更加直接和简单.     

反射倒向随机微分方程的逆比较问题(Ⅰ)

在Briand,Coquet,Hu,Mémin,Peng[1],Coquet,Hu,Mémin,Peng[2],Chen[3],Jiang[8]等中,研究了倒向随机微分方程的逆比较定理,就是通过比较倒向随机微分方程的解来比较倒向随机微分方程的生成元问题.在文[9]中Li和Tang首次研究了反射倒向随机微分方程的逆比较问题.本文考虑在更一般的条件下,反射倒向随机微分方程的生成元的逆比较问题.     

正倒向随机微分方程的适应解及其比较定理

研究了一类正倒向随机微分方程的适应解，其中正向方程不需要满足非退化条件，我们证明了在某些单调条件下，正倒向随机微分方程存在唯一的适应解，并给出了该正倒向随机微分方程的比较定理。     

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。     

关于倒向随机微分方程生成元惟一性的一个结果

在本文中,在假定倒向随机微分方程的标准参数满足较弱条件的前提下,我们证明了倒向随机微分方程的生成元由相对应的倒向随机微分方程的终端条件所得到的初始值惟一决定.这个结果从另一方面也论证和推广了Peng的推测.     

A general comparison theorem for 1-dimensional anticipated BSDEs

Anticipated backward stochastic differential equation (ABSDE) studied the first time in 2007 is a new type of stochastic differential equations. In this paper, we establish a general comparison theorem for ABSDEs.     

Optimal estimation of parameters and states in stochastic time-varying systems with time delay

In this study estimation of parameters and states in stochastic linear and nonlinear delay differential systems with time-varying coefficients and constant delay is explored. The approach consists of first employing a continuous time approximation to approximate the stochastic delay differential equation with a set of stochastic ordinary differential equations. Then the problem of parameter estimation in the resulting stochastic differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman–Bucy filter to the resulting system, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states.     

Nonlinear stochastic differential delay equations

The methods used by Adomian and his co-workers to solve linear and nonlinear stochastic differential equations will be demonstrated to be applicable to differential equations, deterministic or stochastic, involving delays (constant, time dependent, or random).     

Strong convergence in stochastic averaging principle for two time-scales stochastic partial differential equations

The theory of stochastic averaging principle provides an effective approach for the qualitative analysis of stochastic systems with different time-scales and is relatively mature for stochastic ordinary differential equations. In this paper, we study the averaging principle for a class of stochastic partial differential equations with two separated time scales driven by scalar noises. Under suitable assumptions it is shown that the slow component strongly converges to the solution of the corresponding averaged equation.     

Uniqueness and explosion time of solutions of stochastic differential equations driven by fractional Brownian motion

In this paper, we first study the existence and uniqueness of solutions to the stochastic differential equations driven by fractional Brownian motion with non-Lipschitz coefficients. Then we investigate the explosion time in stochastic differential equations driven by fractional Browmian motion with respect to Hurst parameter more than half with small diffusion.     

On the definition of an admitted Lie group for stochastic differential equations

A new definition of an admitted Lie group of transformations for stochastic differential equations involving Brownian motion is presented. The transformation of the dependent variables involves time as well, and it is proved that Brownian motion is transformed to Brownian motion. Applications to a variety of stochastic differential equations are presented.     

Usage of processes with continuous time in the study of stochastic recurrent sequences

The paper proposes a new approach connected with consideration of stochastic difference sequences like sequences of observations (in deterministic or random moments of time) of a continuous time process satisfying a stochastic differential equation.     

随机微分方程数值解在泄洪风险分析中的应用

根据泄洪过程中库水位过程的随机微分方程,利用数值解方法,模拟了随机干扰下的库水位及其波动状况.采用相应公式计算了洪水漫越坝顶事件的概率以及库水位过程在不同时刻的样本均值.并通过比较在同样强度的随机干扰下库水位的高低状况,确定出各种泄洪方案的优劣,从而对防洪工作具有重要的指导意义.     

A priori bound for the supremum of solutions of stable stochastic differential equations

An upper bound for the solutions of stochastic differential equations for which the drift satisfies a usual stability assumption is given. This bound, valid for any time, only needs to make use of explicit constants which can be obtained from the coefficients of these stochastic differential equations. The same kind of result is obtained for Lyapounov functions.