Local limit theorems for ladder epochs
Vladimir Vatutin, Vitali Wachtel
Abstract
Let Sn, n=0,1,2,... be a random walk generated by a sequence of i.i.d. random variables X1, X2,... and let tau be the first descending ladder epoch. Assuming that the distribution of X1 belongs to the domain of attraction of an alpha-stable law, we study the asymptotic behavior of P(tau=n).
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