关于最近无穷维随机泛函微分方程研究的一些看法

Some views on recent randomized study of infinite dimensional functional differential equations

抽象或无穷维随机泛函微分方程是一个相当年幼的学科.本文基于作者近几年对该学科在学习和研究时所获得的一些经验和体会,对问题、方法、技巧、难点和将来工作中要注意的诸多方面提出自己的看法.本文的着眼点主要集中在分析和比较此学科的特点、问题的难点和在处理这些难点时经常使用的方法和工具,同时指出在使用这些方法时应该特别注意的方面.主要的目的是希望通过本文能吸引更多的人进入这个领域,抛砖引玉,从而推动这门学科的发展.

As a relatively new area in mathematics, the subject of abstract or infinite dimensional stochastic functional differential equations is still in its tender age at present. In this note, the author intends to show some of his personal views, mainly based on his own academic experience in this topic, about the current art of research. Special attention is paid to a statement of various methods, techniques and ideas in the undergoing development. What I am trying to do is to highlight the coherent characterization of various difficult problems, effective methods and useful toods frequently seen in this subject. A mild notice is also made on some possible pitfalls which an active researcher working in this area should take into account. It is hoped that, through this short work, some more valuable developments can be promoted and significant progress can be expected in the future.