This volume presents new results in probability theory and partial differential equations related to asymptotic Series: Lectures in Mathematics. ETH Zurich. Num Pages: 154 pages, 2 black & white illustrations, biography. BIC Classification: PBKJ; PBT; PBWL. Category: (P) Professional & Vocational. Dimension: 244 x 170 x 8. Weight in Grams: 600. . 1996. Softcover reprint of the original 1st ed. 1996. Paperback. . . . . Books ship from the US and Ireland.

N� de ref. del art�culo V9783764353926

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T�tulo: Markov Processes and Differential Equations
Editor: Birkhauser Verlag AG
Fecha de publicaci�n: 1996
Idioma: Ingl�s
ISBN 10: 3764353929
ISBN 13: 9783764353926
Encuadernaci�n: Encuadernaci�n de tapa blanda
Estado: New

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Sinopsis

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.

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