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

1999
ISBN: 978-3-540-64435-4
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 220 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1130 g

Reihe: Springer Series in Synergetics

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.

Zielgruppe

Research

Autoren/Hrsg.

Herwaarden, Onno A.

Grasman, Johan

Herwaarden, Onno A., van

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.