scholarly journals Large deviations of convex hulls of planar random walks and Brownian motions

2021 ◽  
Vol 4 ◽  
pp. 1163-1201
Author(s):  
Arseniy Akopyan ◽  
Vladislav Vysotsky
Keyword(s):  
Large Deviations ◽  
Random Walks ◽  
Convex Hulls ◽  
Brownian Motions

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 Convex hulls of multiple random walks: A large-deviation study

2016 ◽  
Vol 94 (5) ◽  
Author(s):  
Timo Dewenter ◽  
Gunnar Claussen ◽  
Alexander K. Hartmann ◽  
Satya N. Majumdar
Keyword(s):  
Random Walks ◽  
Large Deviation ◽  
Convex Hulls

scholarly journals LARGE DEVIATIONS FOR FLOWS OF INTERACTING BROWNIAN MOTIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 315-339 ◽  
Author(s):  
A. A. DOROGOVTSEV ◽  
O. V. OSTAPENKO
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stochastic Flows ◽  
Brownian Motions ◽  
Deviation Principle ◽  
And Brownian Motion

We establish the large deviation principle (LDP) for stochastic flows of interacting Brownian motions. In particular, we consider smoothly correlated flows, coalescing flows and Brownian motion stopped at a hitting moment.

The ruin problem and cover times of asymmetric random walks and Brownian motions

2000 ◽  
Vol 32 (01) ◽  
pp. 177-192 ◽  
Author(s):  
K. S. Chong ◽  
Richard Cowan ◽  
Lars Holst
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Random Walks ◽  
Cover Time ◽  
Brownian Motions ◽  
Brownian Motion With Drift ◽  
And Brownian Motion ◽  
Cover Times ◽  
Ruin Problem

A simple asymmetric random walk on the integers is stopped when its range is of a given length. When and where is it stopped? Analogous questions can be stated for a Brownian motion. Such problems are studied using results for the classical ruin problem, yielding results for the cover time and the range, both for asymmetric random walks and Brownian motion with drift.

scholarly journals Convex hulls of random walks: Large-deviation properties

2015 ◽  
Vol 91 (5) ◽  
Author(s):  
Gunnar Claussen ◽  
Alexander K. Hartmann ◽  
Satya N. Majumdar
Keyword(s):  
Random Walks ◽  
Large Deviation ◽  
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.

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