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

AvJohan Grasman,van Herwaarden, Onno A.

Häftad, Engelska, 2010

Del i serien Springer Series in Synergetics

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Beskrivning

Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation.

Produktinformation

Utgivningsdatum:2010-12-09
Mått:155 x 235 x 14 mm
Vikt:350 g
Format:Häftad
Språk:Engelska
Serie:Springer Series in Synergetics
Antal sidor:220
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783642084096

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Innehållsförteckning

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.