scholarly journals Convex minorants of random walks and Lévy processes

2011 ◽  
Vol 16 (0) ◽  
pp. 423-434 ◽  
Author(s):  
Josh Abramson ◽  
Jim Pitman ◽  
Nathan Ross ◽  
Geronimo Uribe Bravo
Keyword(s):  
Random Walks ◽  
Lévy Processes ◽  
Levy Processes ◽  
Convex Minorants

scholarly journals Lifting Lévy processes to hyperfinite random walks

2006 ◽  
Vol 130 (8) ◽  
pp. 697-706 ◽  
Author(s):  
Sergio Albeverio ◽  
Frederik S. Herzberg
Keyword(s):  
Random Walks ◽  
Lévy Processes ◽  
Levy Processes

scholarly journals Sample path large deviations for Lévy processes and random walks with Weibull increments

2020 ◽  
Vol 30 (6) ◽  
pp. 2695-2739
Author(s):  
Mihail Bazhba ◽  
Jose Blanchet ◽  
Chang-Han Rhee ◽  
Bert Zwart
Keyword(s):  
Large Deviations ◽  
Random Walks ◽  
Lévy Processes ◽  
Sample Path ◽  
Levy Processes ◽  
Sample Path Large Deviations

scholarly journals A New Proof of the Wiener-Hopf Factorization via Basu's Theorem

2012 ◽  
Vol 49 (03) ◽  
pp. 876-882
Author(s):  
Brian Fralix ◽  
Colin Gallagher
Keyword(s):  
Random Walks ◽  
Markov Processes ◽  
Lévy Processes ◽  
Levy Processes ◽  
Specific Class ◽  
Piecewise Deterministic Markov Processes

We illustrate how Basu's theorem can be used to derive the spatial version of the Wiener-Hopf factorization for a specific class of piecewise-deterministic Markov processes. The classical factorization results for both random walks and Lévy processes follow immediately from our result. The approach is particularly elegant when used to establish the factorization for spectrally one-sided Lévy processes.

scholarly journals Sparre Andersen identity and the last passage time

2016 ◽  
Vol 53 (2) ◽  
pp. 600-605 ◽  
Author(s):  
Jevgenijs Ivanovs
Keyword(s):  
Random Walks ◽  
Uniform Distribution ◽  
Lévy Processes ◽  
Passage Time ◽  
Levy Processes ◽  
Last Passage Time ◽  
Random Times

AbstractIt is shown that the celebrated result of Sparre Andersen for random walks and Lévy processes has intriguing consequences when the last time of the process in (-∞, 0], say σ, is added to the picture. In the case of no positive jumps this leads to six random times, all of which have the same distribution—the uniform distribution on [0, σ]. Surprisingly, this result does not appear in the literature, even though it is based on some classical observations concerning exchangeable increments.

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