Nonstandard Methods in Stochastic Analysis and Mathematical Physics
Mathematics Hegh-Krohn Raphael Lindstrom Tom Albeverio Sergio Hoegh-Krohn Raphael Fenstad Jens Erik
ISBN 10: 0486468992 ISBN 13: 9780486468990
Verlag: Dover Publications, Incorporated, 2009
Neu
Softcover
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Beschreibung
Beschreibung:
pp. ix + 514 Illus. Bestandsnummer des Verkäufers 8144876
Inhaltsangabe:
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.
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.
Über die Autorin bzw. den Autor:
Sergio Albeverio is an award-winning mathematical physicist who taught in universities all over the world. Jens Erik Fenstad is a mathematician who taught at the University of Oslo and served as a member of the NATO Science Committee. Raphael Hoegh-Krohn was one of the outstanding mathematical physicists of our age. Tom Lindstrom is a professor of mathematics teaching at the University of Oslo.
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Bibliografische Details
Titel: Nonstandard Methods in Stochastic Analysis ...
Verlag: Dover Publications, Incorporated
Erscheinungsdatum: 2009
Einband: Softcover
Zustand: New