倒向随机微分方程的弱生存性及其应用

倒向随机微分方程的弱生存性及其应用

刘日成¹, 韩月才²,³, 花秋玲²

1. 大庆石油学院数学科学与技术学院, 黑龙江大庆 163318;2. 吉林大学数学学院, 长春 130012; 3. 山东大学数学学院, 济南 250100

收稿日期:2008-06-19 修回日期:1900-01-01 出版日期:2009-05-26 发布日期:2009-06-23
通讯作者: 韩月才

Weak Viability Property of Backward Stochastic DifferentialEquations and Its Application

LIU Richeng¹, HAN Yuecai²,³, HUA Qiu ling²

1. Department of Mathematics Science and Technology, Daqing Petroleum Institute, Daqing 163318, Heilongjiang Province, China; 2. College of Mathematics, Jilin University, Changchun 130012, China;3. College of Mathematics, Shandong University, Jinan 250100, China

Received:2008-06-19 Revised:1900-01-01 Online:2009-05-26 Published:2009-06-23
Contact: HAN Yuecai

摘要/Abstract

摘要： 利用随机Lyapunov方法和Chebychev不等式给出了倒向随机微分方程的解在闭集上具有弱生存性的充分条件, 并获得了一类拟线性抛物偏微分方程的黏性解于非空闭集中具有生存性的判定条件.

关键词: 倒向随机微分方程, 弱生存性, 非线性抛物偏微分方程, 黏性解, 随机Lyapunov泛函

Abstract: The authors investigated the weak viability property of backward stochastic differential equations(shortened by BSWVP). By means of sto chastic Lyapunov’s method and Chebychev’s inequality, the authors give a sufficient condition for BSWVP holds on a nonempty closed set. As application, the authors obtaineda decision condition for the weak viability for the viscosity solution of quasilinear parabolic partial differential equations in a closed set.

Key words: backward stochastic differential equation, weak viability property, quasilinear parabolic PDE, viscosity solution, stochastic Lyapunov functional

中图分类号:

O211

刘日成, 韩月才,, 花秋玲. 倒向随机微分方程的弱生存性及其应用[J]. J4, 2009, 47(03): 519-522.

LIU Richeng, HAN Yuecai,, HUA Qiu ling. Weak Viability Property of Backward Stochastic DifferentialEquations and Its Application[J]. J4, 2009, 47(03): 519-522.