数学
随机微分方程
布朗运动
高斯分布
微分方程
随机偏微分方程
偏微分方程
数学分析
应用数学
统计
物理
量子力学
作者
Peter K. Friz,Martin Hairer
摘要
Introduction.- The space of rough paths.- Brownian motion as a rough path.- Integration against rough paths.- Stochastic integration and Ito's formula.- Doob-Meyer type decomposition for rough paths.- Operations on controlled rough paths.- Solutions to rough differential equations.- Stochastic differential equations.- Gaussian rough paths.- Cameron-Martin regularity and applications.- Stochastic partial differential equations.- Introduction to regularity structures.- Operations on modelled distributions.- Application to the KPZ equation.
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