Approximation Formulas for the Ergodic Moments of Gaussian Random Walk With a Reflecting Barrier

Abstract

In this study, Gaussian random walk process with a generalized reflecting barrier is constructed mathematically. Under some weak conditions, the ergodicity of the process is discussed and exact form of the first four moments of the ergodic distribution is obtained. After, the asymptotic expansions for these moments are established. Moreover, the coefficients of the asymptotic expansions are expressed by means of numerical characteristics of a residual waiting time. © Springer Science+Business Media New York 2013.