登入選單
返回Google圖書搜尋
Nonstandard Methods in Stochastic Analysis and Mathematical Physics
Sergio AlbeverioJens Erik FenstadRaphael Høegh-KrohnTom Lindstrøm
出版Courier Dover Publications, 2009-02-26
主題Mathematics / Mathematical AnalysisMathematics / AppliedScience / Physics / Mathematical & Computational
ISBN04864689929780486468990
URLhttp://books.google.com.hk/books?id=yH71DAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋The Bulletin of the American Mathematical Society acclaimed this text as "a welcome addition" to the literature of nonstandard analysis, a field related to number theory, algebra, and topology. The first half presents a complete and self-contained introduction to the subject, and the second part explores applications to stochastic analysis and mathematical physics.
The text's opening chapters introduce all of the material needed later, including a nonstandard development of the calculus, aspects of singular perturbation theory related to ordinary differential equations, and applications to topology and functional analysis. A significant portion of the text focuses on applications of nonstandard analysis to probability theory. Starting with nonstandard measure theory, the treatment advances to probability problems that can be represented by hyperfinite nonstandard models. Applications of nonstandard analysis to stochastic processes are treated at length, and the authors present numerous applications to mathematical physics. Additional topics include hyperfinite Dirichlet forms and Markov processes, differential operators, and hyperfinite lattice models.