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

作者：Fushiya Hirotaka^*

来源：Journal of Theoretical Probability, 2010, 23(4): 1157-1181.

DOI：10.1007/s10959-009-0244-4

• Sticky
• Reflected random walk
• Weak convergence
• Limit

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.

• 出版日期2010-12