Author	Grasman, Johan. author
Title	Asymptotic Methods for the FokkerโPlanck Equation and the Exit Problem in Applications [electronic resource] / by Johan Grasman, Onno A. van Herwaarden
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999
Connect to	http://dx.doi.org/10.1007/978-3-662-03857-4
Descript	IX, 220 p. online resource

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 Itรด calculus applied to the Langevin equation. The book will be useful to researchers and graduate students

I The FokkerโPlanck Equation -- 1. Dynamical Systems Perturbed by Noise: the Langevin Equation -- 2. The FokkerโPlanck Equation: First Exit from a Domain -- 3. The FokkerโPlanck 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 FokkerโPlanck 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

1. Mathematics
2. Computers
3. Mathematical analysis
4. Analysis (Mathematics)
5. Probabilities
6. Physics
7. Statistical physics
8. Dynamical systems
9. Mathematics
10. Analysis
11. Theory of Computation
12. Probability Theory and Stochastic Processes
13. Statistical Physics
14. Dynamical Systems and Complexity
15. Mathematical Methods in Physics