隨機微分方程:動態(tài)系統(tǒng)方法(英文)
定 價:88 元
叢書名:國外優(yōu)秀數(shù)學著作原版系列
- 作者: [美] 布蘭·霍林斯沃斯(Blane Hollingsworth) 著
- 出版時間:2021/7/1
- ISBN:9787560395135
- 出 版 社:哈爾濱工業(yè)大學出版社
- 中圖法分類:O211.63
- 頁碼:131
- 紙張:膠版紙
- 版次:1
- 開本:32開
《隨機微分方程:動態(tài)系統(tǒng)方法(英文)》是一部英文版的數(shù)學專著,中文書名可譯為《隨機微分方程:動態(tài)系統(tǒng)方法》。
《隨機微分方程:動態(tài)系統(tǒng)方法(英文)》的作者是:布蘭·霍林斯沃斯(Blane Hollingsworth)教授,他于2008年獲得美國奧本大學博士學位。
談到隨機微分方程,不能不提到一位日本數(shù)學家,他就是伊藤清(ItoKiyosi,1915-2008),他精于概率論與函數(shù)解析理論,著有《隨機過程論》(1942)、《概率論基礎(chǔ)》(1944)、《論隨機微分方程》(1953)、《平穩(wěn)隨機分布》(1954)、《迷向隨機流》(1956)、《隨機過程》(1957)、《論隨機過程》(1960)、《擴散過程及樣本路徑》(1965)等。他是許多大獎的得主,而且很長壽,
在中國隨機微分方程成為顯學是緣于彭實戈院士的成功,他創(chuàng)造性的研究了倒向隨機微分方程,并成功的將其應用于金融資產(chǎn)定價問題中,所以是一個既有學術(shù)深度又有廣闊“錢景”的好方向,彭院士也獲得了幾項大獎。
數(shù)學知識每天都在增長,新的發(fā)現(xiàn)和大量的新信息使撰寫全面而翔實的著作變得越來越困難。
《隨機微分方程:動態(tài)系統(tǒng)方法(英文)》是為了解決隨機微分方程(SDE)的基本問題而寫,諸如“什么是隨機微分方程”。事實證明,回答此類基本問題也需要非常有深度的背景知識。
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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