Lattice random walks for sets of random walkers. First passage times

1980 ◽  
Vol 23 (1) ◽  
pp. 11-25 ◽  
Author(s):  
Katja Lindenberg ◽  
V. Seshadri ◽  
K. E. Shuler ◽  
George H. Weiss
Keyword(s):  
Random Walks ◽  
First Passage Times ◽  
First Passage ◽  
Random Walkers ◽  
Lattice Random Walks ◽  
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.

scholarly journals Mean first-passage times of non-Markovian random walkers in confinement

Nature ◽  
2016 ◽  
Vol 534 (7607) ◽  
pp. 356-359 ◽  
Author(s):  
T. Guérin ◽  
N. Levernier ◽  
O. Bénichou ◽  
R. Voituriez
Keyword(s):  
First Passage Times ◽  
First Passage ◽  
Random Walkers ◽  
Mean First Passage Times ◽  
Passage Times

scholarly journals Random walks on random trees

1973 ◽  
Vol 15 (1) ◽  
pp. 42-53 ◽  
Author(s):  
J. W. Moon
Keyword(s):  
Random Walks ◽  
Random Trees ◽  
First Passage Times ◽  
General Reference ◽  
First Passage ◽  
Labelled Trees ◽  
Passage Times

Let T denote one of the nn−2 trees with n labelled nodes that is rooted at a given node x (see [6] or [8] as a general reference on trees). If i and j are any two nodes of T, we write i ∼ j if they are joined by an edge in T. We want to consider random walks on T; we assume that when we are at a node i of degree d the probability that we proceed to node j at the next step is di–1 if i ∼ j and zero otherwise. Our object here is to determine the first two moments of the first return and first passage times for random walks on T when T is a specific tree and when T is chosen at random from the set of all labelled trees with certain properties.

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