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

Johan Grasman, Onno A. Herwaarden van (Autoren)

Buch | Softcover

IX, 220 Seiten

2010 | 1. Softcover reprint of hardcover 1st ed. 1999
Springer Berlin (Verlag)
978-3-642-08409-6 (ISBN)

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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.

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	9.12.2010
Reihe/Serie	Springer Series in Synergetics
Zusatzinfo	IX, 220 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	357 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	3-642-08409-5 / 3642084095
ISBN-13	978-3-642-08409-6 / 9783642084096
Zustand	Neuware