Local limit theorems for ladder epochs
arXiv:math/0701914
Abstract
Let {S_n, n=0,1,2,...} be a random walk generated by a sequence of i.i.d. random variables X_1, X_2,... and let tau be the first descending ladder epoch. Assuming that the distribution of X_1 belongs to the domain of attraction of an alpha-stable law, we study the asymptotic behavior of P(tau=n).
21 pages