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AuthorGrasman, Johan. author
TitleAsymptotic Methods for the Fokkerโ{128}{148}Planck Equation and the Exit Problem in Applications [electronic resource] / by Johan Grasman, Onno A. van Herwaarden
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999
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Descript IX, 220 p. online resource


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 Itรด calculus applied to the Langevin equation. The book will be useful to researchers and graduate students


I The Fokkerโ{128}{148}Planck Equation -- 1. Dynamical Systems Perturbed by Noise: the Langevin Equation -- 2. The Fokkerโ{128}{148}Planck Equation: First Exit from a Domain -- 3. The Fokkerโ{128}{148}Planck Equation: One Dimension -- II Asymptotic Solution of the Exit Problem -- 4. Singular Perturbation Analysis of the Differential Equations for the Exit Probability and Exit Time in One Dimension -- 5. The Fokkerโ{128}{148}Planck Equation in Several Dimensions: the Asymptotic Exit Problem -- III Applications -- 6. Dispersive Groundwater Flow and Pollution -- 7. Extinction in Systems of Interacting Biological Populations -- 8. Stochastic Oscillation -- 9. Confidence Domain, Return Time and Control -- 10. A Markov Chain Approximation of the Stochastic Dynamical System -- Literature -- Answers to Exercises -- Author Index

Mathematics Computers Mathematical analysis Analysis (Mathematics) Probabilities Physics Statistical physics Dynamical systems Mathematics Analysis Theory of Computation Probability Theory and Stochastic Processes Statistical Physics Dynamical Systems and Complexity Mathematical Methods in Physics


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