Synopses & Reviews
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.
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 self-contained introduction to the subject, and the second part explores applications to stochastic analysis and mathematical physics. 1986 edition.
Synopsis
Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." Bulletin of the American Mathematical Society. 1986 edition.
Table of Contents
PrefacePart I. Basic Course1. Calculus2. Topology and Linear Spaces3. ProbabilityPart II. Selected Applications4. Stochastic Analysis5. Hyperfinite Dirichlet Forms and Markov Processes6. Topics in Differential Operators7. Hyperfinite Lattice Models