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Markov Chains on Graphs and Brownian Motion

Author

Listed:
  • Nathanaël Enriquez

    (Université de Paris 6)

  • Yuri Kifer

    (Hebrew University)

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.

Suggested Citation

  • Nathanaël Enriquez & Yuri Kifer, 2001. "Markov Chains on Graphs and Brownian Motion," Journal of Theoretical Probability, Springer, vol. 14(2), pages 495-510, April.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:2:d:10.1023_a:1011119932045
    DOI: 10.1023/A:1011119932045
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