Asymptotic results on the maximal deviation of simple random walks
Let \((X_ n)\) be a simple random walk on the set of integers. The authors study the conditional distributions of \({}^+D_ n=\max \{X_ k:0\leq k\leq n\}\) and \(D_ n=\max \{| X_ k|:0\leq k\leq n\}\) on the hypotheses \(X_ n=X_ 0=0\). They obtain explicit formulas as well as asymptotic results for the distribution functions and the moments.
scientific article; zbMATH DE number 3878109
scientific article