scholarly journals Exact expressions of mean first-passage times and splitting probabilities for random walks in bounded rectangular domains

2006 ◽  
Vol 124 (20) ◽  
pp. 206103 ◽  
Author(s):  
S. Condamin ◽  
O. Bénichou
Keyword(s):  
Random Walks ◽  
First Passage Times ◽  
First Passage ◽  
Mean First Passage Times ◽  
Passage Times

scholarly journals Correlation functions, mean first passage times, and the Kemeny constant

2020 ◽  
Vol 152 (10) ◽  
pp. 104108 ◽  
Author(s):  
Adam Kells ◽  
Vladimir Koskin ◽  
Edina Rosta ◽  
Alessia Annibale
Keyword(s):  
Correlation Functions ◽  
First Passage Times ◽  
First Passage ◽  
Mean First Passage Times ◽  
Passage Times

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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