Nonstandard Methods in Stochastic Analysis and Mathematical Physics

ISBN-13: 9780486468990 / Angielski / Miękka / 2009 / 528 str.

Sergio Albeverio; Jens Erik Fenstad; Raphael Hoegh-Krohn

Opis

The Bulletin of the American Mathematical Society acclaimed this text as "a welcome addition" to the literature of nonstandard analysis, a field related tonumber theory, algebra, and topology. The first half presents acomplete and self-contained introduction to the subject, and the second part exploresapplications 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."