Local limit theorems for ladder moments [report]

Vladimir Vatutin, Vitali Wachtel, University, My, University, My
Let So = O,{Sn}n≥1 be a random walk generated by a sequence of i.i.d. random variables X1,X2,... and let [tau] ̄:= min{n ≥ 1 : Sn ≤ O} and [tau]+ := min{n ≥ 1 : Sn > 0}. Assuming that the distribution of X1 belongs to the domain of attraction of an [alpha]-stable law, [alpha]≠1, we study the asymptotic behavior of P([tau]±=n) as n → ∞.
doi:10.34657/2598 fatcat:jccyoqqp3vhbrf657wljfu2gt4