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
DOI
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 $nrightarrowinfty.$
Download Documents