Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications
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Beschreibung
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 Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.
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.
This is probably the first monograph that treats the asympotic methods which are eminently important for practical applications Includes supplementary material: sn.pub/extras
Autor*in
Johan Grasman
Themen in »Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications«
Approximation Boundary value problem Fokker-Planck equation Markov Markov chain calculus differential equation dynamical systems dynamische Systeme