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Random Perturbations of Hamiltonian Systems
Mark I. Freidlin and Alexander D. Wentzell

Memoirs of the American Mathematical Society
1994; 82 pp; softcover
Volume: 109
ISBN-10: 0-8218-2586-0
ISBN-13: 978-0-8218-2586-0
List Price: US$39
Individual Members: US$23.40
Institutional Members: US$31.20
Order Code: MEMO/109/523
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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

  • Introduction
  • Main results
  • Proof of Theorem 2.2
  • Proofs of Lemmas 3.2, 3.3, 3.4
  • Proof of Lemma 3.5
  • References
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