ADAPTED SOLUTION OF A BACKWARD STOCHASTIC DIFFERENTIAL-EQUATION

被引：1726

作者：

PARDOUX, E

PENG, SG

机构：

[1] SHANDONG UNIV,INST MATH,JINAN,PEOPLES R CHINA

[2] UNIV AIX MARSEILLE 1,URA 225,F-13331 MARSEILLE 3,FRANCE

[3] INST NATL RECH INFORMAT & AUTOMAT,F-78153 LE CHESNAY,FRANCE

[4] FUDAN UNIV,INST MATH,SHANGHAI,PEOPLES R CHINA

来源：

SYSTEMS & CONTROL LETTERS | 1990年 / 14卷 / 01期

关键词：

adapted process; Backward stochastic differential equation;

D O I：

10.1016/0167-6911(90)90082-6

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Let Wt; t ε{lunate} [0, 1] be a standard k-dimensional Weiner process defined on a probability space (Ω, F, P), and let Ft denote its natural filtration. Given a F1 measurable d-dimensional random vector X, we look for an adapted pair of processes {x(t), y(t); t ε{lunate} [0, 1]} with values in Rd and Rd×k respectively, which solves an equation of the form: x(t) + ∫ t 1f(s, x(s), y(s)) ds + ∫ t 1 [g(s, x(s)) + y(s)] dWs = X. A linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process. We also generalize our results to the following equation: x(t) + ∫ t 1f(s, x(s), y(s)) ds + ∫ t 1 g(s, x(s)) + y(s)) dWs = X under rather restrictive assumptions on g. © 1990.

引用

页码：55 / 61

页数：7