線性正倒向隨機微分方程與里卡蒂方程

Abstract

本篇論文中我們探討線性正倒向隨機微分方程的可解性。我們在本篇論文中我們探討特殊情形時( b A = O)，可解性的充分必要條件。我們是針對Ma & Yong (2000)工作的延伸。最後我們提出了一個正向微分方程與倒向微分方程的關係，藉由解一個矩陣的常微分方程(里卡蒂方程)提出了類似的充分必要條件。

In this paper we investigate the solvability of linear forward-backward stochastic differential equations (FBSDEs, for short). We give sufficient and necessary conditions of the solvability in linear forward-backward stochastic differential equations and prove it in a special case ($widehat A=O$). These results are extensional work of Ma & Yong (2000). Then we introduce the relationship between forward equation and backward equation, we also can get similar sufficient and necessary conditions to solve linear forward-backward stochastic differential equations by solving a matrix ordinary differential equation (a Riccati type equation).