Diffusion Processes on Graphs and the Averaging Principle

Authors:
  • MFMark I. Freidlin
    Mark I. Freidlin
  • AWAlexander D. Wentzell
    Alexander D. Wentzell
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Abstract
A number of asymptotic problems for "classical" stochastic processes leads to diffusion processes on graphs. In this paper we study several such examples and develop a general technique for these problems. Diffusion in narrow tubes, processes with fast transmutations and small random perturbations of Hamiltonian systems are studied.