Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications - Johan Grasman, Onno A. Herwaarden  van

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

Buch | Hardcover
IX, 220 Seiten
1999 | 1999
Springer Berlin (Verlag)
978-3-540-64435-4 (ISBN)
80,24 inkl. MwSt
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.

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.

Erscheint lt. Verlag 8.3.1999
Reihe/Serie Springer Series in Synergetics
Zusatzinfo IX, 220 p.
Verlagsort Berlin
Sprache englisch
Maße 156 x 234 mm
Gewicht 520 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Naturwissenschaften Physik / Astronomie Astronomie / Astrophysik
Naturwissenschaften Physik / Astronomie Theoretische Physik
Schlagworte Approximation • Boundary value problem • Calculus • differential equation • Dynamical Systems • Dynamische Systeme • Fokker-Planck Equation • Markov • Markov Chain
ISBN-10 3-540-64435-0 / 3540644350
ISBN-13 978-3-540-64435-4 / 9783540644354
Zustand Neuware
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