Del i serien Springer Series in Synergetics

Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications

Häftad, Engelska, 2010

AvJohan Grasman,van Herwaarden, Onno A.

719 kr

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

Produktinformation

Utgivningsdatum2010-12-09
Mått155 x 235 x 14 mm
Vikt350 g
FormatHäftad
SpråkEngelska
SerieSpringer Series in Synergetics
Antal sidor220
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783642084096

Tillhör följande kategorier

I The Fokker—Planck Equation.- 1. Dynamical Systems Perturbed by Noise: the Langevin Equation.- 2. The Fokker—Planck Equation: First Exit from a Domain.- 3. The Fokker—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 Fokker—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.

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