Properties of a functional of trajectories which arises in studying the probabilities of large deviations of random walks

2011 ◽  
Vol 52 (4) ◽  
pp. 612-627 ◽  
Author(s):  
A. A. Borovkov ◽  
A. A. Mogul’skiĭ
Keyword(s):  
Large Deviations ◽  
Random Walks ◽  
Probabilities Of Large Deviations

scholarly journals Large deviations of convex hulls of self-avoiding random walks

2018 ◽  
Vol 97 (6) ◽  
Author(s):  
Hendrik Schawe ◽  
Alexander K. Hartmann ◽  
Satya N. Majumdar
Keyword(s):  
Large Deviations ◽  
Random Walks ◽  
Convex Hulls

scholarly journals Asymptotics for the First Passage Times of Lévy Processes and Random Walks

2013 ◽  
Vol 50 (1) ◽  
pp. 64-84 ◽  
Author(s):  
Denis Denisov ◽  
Vsevolod Shneer
Keyword(s):  
Large Deviations ◽  
Random Walks ◽  
Levy Processes ◽  
Levy Process ◽  
First Passage Times ◽  
Exact Asymptotics ◽  
First Passage ◽  
Heavy Tailed ◽  
First Time ◽  
Passage Times

We study the exact asymptotics for the distribution of the first time, τx, a Lévy process Xt crosses a fixed negative level -x. We prove that ℙ{τx >t} ~V(x) ℙ{Xt≥0}/t as t→∞ for a certain function V(x). Using known results for the large deviations of random walks, we obtain asymptotics for ℙ{τx>t} explicitly in both light- and heavy-tailed cases.

Sign in / Sign up

Export Citation Format

Share Document