Asymptotics of moments of local times of a random walk (Q1096255)

Let \((S_ k\); \(k\in {\mathbb{N}})\) be a one-dimensional, aperiodic recurrent random walk starting from zero, and let \(\xi\) (x,n) be the number of times the random walk hits the point x in n steps. \(\xi\) (x,n) is usually called the local time of the random walk. Recently A. N. Borodin obtained the optimal rate for the convergence of the distribution of \(n^{-}\xi (x,n)\) to the distribution of the Brownian local time. In this article the author gets convergence rates for the moments of \(n^{-}\xi (x,n)\) under the assumption that E \(\xi\) (x,n)\({}^ 3<\infty\).