Memoirs of the American Mathematical Society 1994; 82 pp; softcover Volume: 109 ISBN10: 0821825860 ISBN13: 9780821825860 List Price: US$39 Individual Members: US$23.40 Institutional Members: US$31.20 Order Code: MEMO/109/523
 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 whitenoise 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. Readership 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
