A limit theorem for diffusions on graphs with variable configuration

2007/01/23 by Alexey M. Kulik, Kulik, Alexey M.
Mathematics · #60F17 #60H10 #60J60 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F17 #msc:60H10 #msc:60J60

paper · pdf · doi:10.48550/arxiv.math/0701632

18 pages, 2 figures

arxiv created 2007/01/23 · arxiv updated 2009/12/01

Abstract

A limit theorem for a sequence of diffusion processes on graphs is proved in a case when vary both parameters of the processes (the drift and diffusion coefficients on every edge and the asymmetry coefficients in every vertex), and configuration of graphs, where the processes are set on. The explicit formulae for the parameters of asymmetry for the vertices of the limiting graph are given in the case, when, in the pre-limiting graphs, some groups of vertices form knots contracting into a points.

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