Random perturbations of Hamiltonian systems
About this Title
Mark I. Freidlin and Alexander D. Wentzell
Publication: Memoirs of the American Mathematical Society
Publication Year 1994: Volume 109, Number 523
ISBNs: 978-0-8218-2586-0 (print); 978-1-4704-0100-9 (online)
MathSciNet review: 1201269
MSC (1991): Primary 35K15; Secondary 34C37, 34F05, 35J25, 60J60, 70H05
Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.
Specialists in dynamical systems, partial differential equations, probability theory and control theory.
Table of Contents
- 1. Introduction
- 2. Main results
- 3. Proof of Theorem 2.2
- 4. Proofs of Lemmas 3.2, 3.3, 3.4
- 5. Proof of Lemma 3.5