Author | Grasman, Johan. author |
---|---|

Title | Asymptotic Methods for the Fokkerโ{128}{148}Planck 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 |

SUMMARY

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

CONTENT

I The Fokkerโ{128}{148}Planck Equation -- 1. Dynamical Systems Perturbed by Noise: the Langevin Equation -- 2. The Fokkerโ{128}{148}Planck Equation: First Exit from a Domain -- 3. The Fokkerโ{128}{148}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 Fokkerโ{128}{148}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

Mathematics
Computers
Mathematical analysis
Analysis (Mathematics)
Probabilities
Physics
Statistical physics
Dynamical systems
Mathematics
Analysis
Theory of Computation
Probability Theory and Stochastic Processes
Statistical Physics Dynamical Systems and Complexity
Mathematical Methods in Physics