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Local limit theorems for ladder epochs

Research paper by Vladimir Vatutin, Vitali Wachtel

Indexed on: 31 Jan '07Published on: 31 Jan '07Published in: Mathematics - Probability



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).