WIAS Preprint No. 1200, (2007)

Local limit theorems for ladder moments



Authors

  • Vatutin, Vladimir
  • Wachtel, Vitali

2010 Mathematics Subject Classification

  • 60G50 60G40

Keywords

  • Random walk, ladder moment, Spitzer condition

Abstract

Let $S_0=0,S_n_ngeq1$ be a random walk generated by a sequence of i.i.d. random variables $X_1,X_2,...$ and let $tau^-:=minleft ngeq1: S_nleq0right $ and $tau^+:=minleft ngeq 1: S_n>0right $. Assuming that the distribution of $X_1$ belongs to the domain of attraction of an $alpha$-stable law$,alphaneq1,$ we study the asymptotic behavior of $mathbbP(tau^pm=n)$ as $nrightarrowinfty.$

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