The Local Asymptotics of the Overshoot of a Delay Random Walk

2019 ◽  
Vol 08 (02) ◽  
pp. 370-374
Author(s):  
甜甜 胡
Keyword(s):  
Random Walk ◽  
Local Asymptotics

The Uniform Local Asymptotics of the Overshoot of a Random Walk with Heavy-Tailed Increments

2009 ◽  
Vol 25 (3) ◽  
pp. 508-521 ◽  
Author(s):  
Guochun Chen ◽  
Yuebao Wang ◽  
Fengyang Cheng
Keyword(s):  
Random Walk ◽  
Local Asymptotics ◽  
Heavy Tailed

scholarly journals Local asymptotics for the area of random walk excursions

2015 ◽  
Vol 91 (2) ◽  
pp. 495-513 ◽  
Author(s):  
Denis Denisov ◽  
Martin Kolb ◽  
Vitali Wachtel
Keyword(s):  
Random Walk ◽  
Local Asymptotics

scholarly journals Local asymptotics of the cycle maximum of a heavy-tailed random walk

2007 ◽  
Vol 39 (1) ◽  
pp. 221-244 ◽  
Author(s):  
Denis Denisov ◽  
Vsevolod Shneer
Keyword(s):  
Random Walk ◽  
Positive Constant ◽  
Random Variables ◽  
Heavy Tailed Distribution ◽  
Local Asymptotics ◽  
Cycle Maximum ◽  
Heavy Tailed ◽  
Independent And Identically Distributed

Let ξ, ξ1, ξ2,… be a sequence of independent and identically distributed random variables, and let Sn=ξ1+⋯+ξn and Mn=maxk≤nSk. 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 ∈ (x, x+T]} as x→∞, for a fixed, positive constant T.

scholarly journals Local asymptotics for the area under the random walk excursion

2018 ◽  
Vol 50 (2) ◽  
pp. 600-620
Author(s):  
Elena Perfilev ◽  
Vitali Wachtel
Keyword(s):  
Random Walk ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Tail Behaviour ◽  
Local Asymptotics ◽  
Negative Drift ◽  
Local Central Limit Theorem

Abstract We study the tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and light-tailed increments. We determine the asymptotics for local probabilities for the area and prove a local central limit theorem for the duration of the excursion conditioned on the large values of its area.

scholarly journals Local asymptotics of the cycle maximum of a heavy-tailed random walk

2007 ◽  
Vol 39 (01) ◽  
pp. 221-244 ◽  
Author(s):  
Denis Denisov ◽  
Vsevolod Shneer
Keyword(s):  
Random Walk ◽  
Positive Constant ◽  
Random Variables ◽  
Heavy Tailed Distribution ◽  
Local Asymptotics ◽  
Cycle Maximum ◽  
Heavy Tailed ◽  
Independent And Identically Distributed

Let ξ, ξ1, ξ2,… be a sequence of independent and identically distributed random variables, and let S n =ξ1+⋯+ξ n and M n =max k≤n S k . Let τ=min{n≥1: S n ≤0}. We assume that ξ has a heavy-tailed distribution and negative, finite mean E(ξ)&lt;0. We find the asymptotics of P{Mτ ∈ (x, x+T]} as x→∞, for a fixed, positive constant T.

Elements of the Random Walk

2004 ◽  
Author(s):  
Joseph Rudnick ◽  
George Gaspari
Keyword(s):  
Random Walk
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