Rate of Weak Convergence of Random Walk with a Generalized Reflecting Barrier

Abstract

In this study, a random walk process with generalized reflecting barrier is considered and an inequality for rate of weak convergence of the stationary distribution of the process of interest is propounded. Though the rate of convergence is not thoroughly examined, the literature does provide a weak convergence theorem under certain conditions for the stationary distribution of the process under consideration. Nonetheless, one of the most crucial issues in probability theory is the convergence rate in limit theorems, as it affects the precision and effectiveness of using these theorems in practice. Therefore, for the rate of convergence for the examined process, comparatively simple inequality is represented. The obtained inequality demonstrates that the rate of convergence is correlated with the tail of the distribution of ladder heights of the random walk.