《随机微分方程：动态系统方法（英文）》是一部英文版的数学专著，中文书名可译为《随机微分方程：动态系统方法》。
《随机微分方程：动态系统方法（英文）》的作者是：布兰·霍林斯沃斯（Blane Hollingsworth）教授，他于2008年获得美国奥本大学博士学位。
谈到随机微分方程，不能不提到一位日本数学家，他就是伊藤清（ItoKiyosi，1915-2008），他精于概率论与函数解析理论，著有《随机过程论》（1942）、《概率论基础》（1944）、《论随机微分方程》（1953）、《平稳随机分布》（1954）、《迷向随机流》（1956）、《随机过程》（1957）、《论随机过程》（1960）、《扩散过程及样本路径》（1965）等。他是许多大奖的得主，而且很长寿，
在中国随机微分方程成为显学是缘于彭实戈院士的成功，他创造性的研究了倒向随机微分方程，并成功的将其应用于金融资产定价问题中，所以是一个既有学术深度又有广阔“钱景”的好方向，彭院士也获得了几项大奖。
数学知识每天都在增长，新的发现和大量的新信息使撰写全面而翔实的著作变得越来越困难。
《随机微分方程：动态系统方法（英文）》是为了解决随机微分方程（SDE）的基本问题而写，诸如“什么是随机微分方程”。事实证明，回答此类基本问题也需要非常有深度的背景知识。
Mathematics knowledge grows every day; new discoveries and overwhelming amounts of new information make it more and more difficult to write comprehensive yet informative texts. This one developed as an attempt to pin down the basics of stochastic differential equations （SDE's）， simple questions like， \"What is a stochastic differential equation?\" It turns out the depth behind the requisite knowledge to answer such an elementary question is quite substantial.
Many great texts already exist that attack SDE's from the stochastic perspective， but our main objective is to present the material from the dynamical systems perspective， aimed at the audience familiar with classical analysis and differential equations. Really， my advisor Paul Schmidt at Auburn University had the idea of presenting the material from a \"new cultural perspective\" and his contribution to this work is enormous. We feel that this presentation will help mathematicians understand， with a minimum of technicality， what SDE's are， and if they are appropriate for their particular modeling/applications.
1 INTRODUCTION AND PRELIMINARIES
1．1 Stochastic Processes and Their Distributions
1．2 Semigroups of Linear Operators
1．3 Kernels and Semigroups of Kernels
1．4 Conditional Expectation， Martingales， and Markov Processes
1．5 Brownian Motion
2 ITO INTEGRALS AND STOCHASTIC DIFFERENTIAL EQUATIONS
2．1 The Ito Integral
2．2 Stochastic Differential Equations and their Solutions
2．3 Ito's Formula and Examples
3 DYNAMICAL SYSTEMS AND STOCHASTIC STABILITY
3．1 \"Stochastic Dynamical Systems\"
3．2 Koopman and Frobenius-Perron Operators： The Deterministic Case
3．3 Koopman and Frobenius-Perron Operators： The Stochastic Case
3．4 Liapunov Stability
3．5 Markov Semigroup Stability
3．6 Long-time behavior of a stochastic predator-prey model
BIBLIOGRAPHY
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