Markov Chains on Graphs and Brownian Motion

Nathanaël Enriquez () and Yuri Kifer ()
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Nathanaël Enriquez: Université de Paris 6
Yuri Kifer: Hebrew University

Journal of Theoretical Probability, 2001, vol. 14, issue 2, 495-510

Abstract: Abstract We consider random walks with small fixed steps inside of edges of a graph $${\mathcal{G}}$$ , prescribing a natural rule of probabilities of jumps over a vertex. We show that after an appropriate rescaling such random walks weakly converge to the natural Brownian motion on $${\mathcal{G}}$$ constructed in Ref. 1.

Keywords: random walks; invariance principle; Brownian motion on graphs (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1011119932045

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