高阶偏微分方程与概率方法

High Order Partial Differential Equations and Probabilistic Methods

二阶偏微分方程与扩散过程的联系是概率界众所周知的．前者为后者提供了分析依据，后者为前者的解给出了概率表示．如何把这种联系推广到高阶偏微分方程的情形，是很多概率学家近十几年来一直关心的问题．本文试就此问题介绍有关的情况及一些最新进展，从中不难发现很多重要问题有待解决，期望能够引起同行的注意．

It is well known that the close connection between the second order partial differential equations and diffusion processes. The theory on the second order partial differential equations provides analytic background for the study of diffusion processes,meanwhile by running diffusion processes we can give a simple,intuitive probabilistic representation for solutions to the second order partial differential equations. Many people have been attempting to extend such connection to the case of high order partial differential equations in the recent decades.This article is devoted to introducing some results and the latest progress in this research field.It is easy to find plenty of interesting problems requiring further studying.