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Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications [electronic resource] by Grasman, Johan, Herwaarden, Onno A is a book available to read on EtoBox.

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Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems where noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the It? calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.Content: Front Matter....Pages I-IXFront Matter....Pages 1-1Dynamical Systems Perturbed by Noise: the Langevin Equation....Pages 3-17The Fokker—Planck Equation: First Exit from a Domain....Pages 18-26The Fokker—Planck Equation: One Dimension....Pages 27-39Front Matter....Pages 41-41Singular Perturbation Analysis of the Differential Equations for the Exit Probability and Exit Time in One Dimension....Pages 43-72The Fokker—Planck Equation in Several Dimensions: the Asymptotic Exit Problem....Pages 73-96Front Matter....Pa

Author

Grasman, Johan, Herwaarden, Onno A

Publisher

Berlin, Heidelberg : Springer Berlin Heidelberg

Published

1999

Language

EN