Overview
- The comprehensive presentation serves as an excellent basis for a Master's course on stochastic partial differential equations(SPDEs) with Lévy noise
- The showcase character of this study provides particular insight into the methods developed and stimulates future research
- An additional chapter connects the mathematical results to its climatological motivation
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2085)
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Table of contents (7 chapters)
Keywords
About this book
This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.
Authors and Affiliations
Bibliographic Information
Book Title: The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
Authors: Arnaud Debussche, Michael Högele, Peter Imkeller
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-00828-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2013
Softcover ISBN: 978-3-319-00827-1Published: 14 October 2013
eBook ISBN: 978-3-319-00828-8Published: 01 October 2013
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIV, 165
Number of Illustrations: 1 b/w illustrations, 8 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Dynamical Systems and Ergodic Theory, Partial Differential Equations