LOCAL ASYMPTOTICS OF THE CYCLE MAXIMUM OF A HEAVY-TAILED RANDOM WALK.

Autor:	Denisov, Denis, Shneer, Vsevolod
Předmět:	RANDOM walks RANDOM variables ASYMPTOTIC expansions NUMERICAL analysis ASYMPTOTIC distribution DISTRIBUTION (Probability theory)
Zdroj:	Advances in Applied Probability; Mar2007, Vol. 39 Issue 1, p221-224, 24p
Abstrakt:	Let ξ, ξ1, ξ2, be a sequence of independent and identically distributed random variables, and let Sn =ξ1 +…+ξn and Mn = maxk⩽n Sk. Let τ =min{n⩾1: Sn ⩽0|. We assume that ξ has a heavy-tailed distribution and negative, finite mean E(ξ) < 0. We find the asymptotics of P{Mτ ϵ (x, x + T]| as × → ∞, for a fixed, positive constant T. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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