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Weak Convergence Theorem of a Nonnegative Random Walk to Sticky Reflected Brownian Motion

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  • Hirotaka Fushiya

    (Aoyama Gakuin University)

Abstract

We obtain a convergence theorem of a 1-dimensional sticky reflected random walk with state space R +. It behaves like a random walk if it is away from the origin. Once it reaches 0, it stays at 0 for a while and is then repelled to the positive region. We consider its tightness and a martingale problem for a discontinuous function in order to construct a weak convergence theorem.

Suggested Citation

  • Hirotaka Fushiya, 2010. "Weak Convergence Theorem of a Nonnegative Random Walk to Sticky Reflected Brownian Motion," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1157-1181, December.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:4:d:10.1007_s10959-009-0244-4
    DOI: 10.1007/s10959-009-0244-4
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    References listed on IDEAS

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    1. Amir, Madjid, 1991. "Sticky Brownian motion as the strong limit of a sequence of random walks," Stochastic Processes and their Applications, Elsevier, vol. 39(2), pages 221-237, December.
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