Nonstandard Methods in Stochastic Analysis and Mathematical Physics (Pure and Applied Mathematics)

Sergio Alberverio

ISBN 10: 0120488612 / ISBN 13: 9780120488612

Published by Academic Pr, 1986

About this Item

Nonstandard Methods in Stochastic Analysis and Mathematical Physics (Pure and Applied Mathematics) by Sergio Alberverio. Academic Pr, 1986. 514pp. Language: English. Condition Notes: Note: Unused or barely used with light shelfwear and minor cosmetic defects.

Seller Inventory # 00029985

Bibliographic Details

• Title: Nonstandard Methods in Stochastic Analysis and Mathematical Physics (Pure and Applied Mathematics)
• Publisher: Academic Pr
• Publication Date: 1986
• Language: English
• ISBN 10: 0120488612
• ISBN 13: 9780120488612
• Binding: Paperback
• Condition: Very Good

About this title

Synopsis

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.