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

Hirotaka Fushiya ()
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Hirotaka Fushiya: Aoyama Gakuin University

Journal of Theoretical Probability, 2010, vol. 23, issue 4, 1157-1181

Abstract: 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.

Keywords: Sticky; Reflected random walk; Weak convergence; Limit; 60B10 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0244-4

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