Markov Processes and Differential Equations: Asymptotic Problems (Lectures in Mathematics. ETH Zurich)

Mark Freidlin

ISBN 10: 3764353929 / ISBN 13: 9783764353926

Verlag: Birkhauser Basel, 1996

Beschreibung

152 pp., Paperback, NEW!! - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.

Bestandsnummer des Verkäufers ZB1250044

Bibliografische Details

• Titel: Markov Processes and Differential Equations: Asymptotic Problems (Lectures in Mathematics. ETH Zurich)
• Verlag: Birkhauser Basel
• Veröffentlichungsdatum: 1996
• Sprache: Englisch
• ISBN-10: 3764353929
• ISBN-13: 9783764353926
• Bindung: Softcover
• Zustand: New

Über diesen Titel

Inhaltsangabe

Probabilistic methods can be applied very successfully to a number of asymptotic problems for second-order linear and non-linear partial differential equations. Due to the close connection between the second order differential operators with a non-negative characteristic form on the one hand and Markov processes on the other, many problems in PDE's can be reformulated as problems for corresponding stochastic processes and vice versa. In the present book four classes of problems are considered: - the Dirichlet problem with a small parameter in higher derivatives for differential equations and systems - the averaging principle for stochastic processes and PDE's - homogenization in PDE's and in stochastic processes - wave front propagation for semilinear differential equations and systems. From the probabilistic point of view, the first two topics concern random perturbations of dynamical systems. The third topic, homog- enization, is a natural problem for stochastic processes as well as for PDE's. Wave fronts in semilinear PDE's are interesting examples of pattern formation in reaction-diffusion equations. The text presents new results in probability theory and their applica- tion to the above problems. Various examples help the reader to understand the effects. Prerequisites are knowledge in probability theory and in partial differential equations.