摘要
随机偏微分方程(SPDE)是目前国内外广泛关注研究进展迅速的一个活跃的学术研究领域.该主题的研究涉及概率论(随机分析、随机场)、偏微分方程、调和分析等诸多分支学科方向.特别是随机偏微分方程其背景更多地源于现代物理学、化学、生物学、经济学等应用性学科,这使得该领域的研究显示出较强的意义和活力.本文从超布朗运动研究出发,发展性地提出有较强背景意义的典型类随机偏微分方程,并进而过渡到一般及更广泛类的随机偏微分方程的研究.同时我们系统地总结了关于高阶随机偏微分方程和随机波动方程的研究成果.
The stochastic partial differential equation（abbr.SPDE） has recently aroused widely attentions,which has been becoming an active field with rapidly increasing interests.The topic involves probability theory（stochastic analysis,stochastic field）,partial differential equation, harmonic analysis etc.Especially,SPDE motivated by some phenomenon from modern physics,chemistry,biology and economics etc.This makes the subject research much more significant. In this paper,we start at the super-Brownian motion and propose some typical SPDEs with strong background,and then we consider the general stochastic partial differential equations. We systematically summarized our recent results on the high-order stochastic parabolic equations and stochastic wave equations.
出处
《数学进展》
CSCD
北大核心
2010年第4期385-398,共14页
Advances in Mathematics（China）
基金
国家自然科学基金(No.10871103)
关键词
超布朗运动
随机偏微分方程
随机波动方程
super-Brownian motion
stochastic parabolic equations
stochastic wave equations
