Local limit theorems for ladder epochs

2007/01/31 by Vatutin, Vladimir, Wachtel, Vitali
#60G50 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/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 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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