Conditioning subordinators embedded in Markov processes
TLDR
In this paper, the running infimum of a Levy process relative to its point of issue is known to have the same range that of the negative of a certain subordinator, and the problem of conditioning a subordinator to remain in a strip is considered.About:
This article is published in Stochastic Processes and their Applications.The article was published on 2017-04-01 and is currently open access. It has received 9 citations till now. The article focuses on the topics: Subordinator & Markov process.read more
Citations
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Conditioned real self-similar Markov processes
TL;DR: In this article, the authors show that the specific case of conditioning to avoid the origin corresponds to a classical Cramer-Esscher-type transform to the Markov Additive Process (MAP) that underlies the Lamperti-Kiu representation of a real self-similar Markov process.
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Stable processes conditioned to avoid an interval
TL;DR: In this paper, it was shown that conditioning stable Markov processes to avoid an interval is possible in the classical sense and that the resulting process is a Doob h -transform of the stable process killed on entering the aforesaid interval.
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Stable processes conditioned to avoid an interval
TL;DR: In this article, it was shown that conditioning stable Markov processes to avoid an interval is possible in the classical sense and that the resulting process is a Doob $h$-transform of the stable process killed on entering the aforesaid interval.
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Deep Factorisation of the Stable Process III: the View from Radial Excursion Theory and the Point of Closest Reach
TL;DR: In this article, the authors compute the distribution of the point of closest reach to the origin in the path of any d-dimensional isotropic stable process, with d ≥ 2, and develop a new radial excursion theory from which they push the classical Blumenthal-Getoor-Ray identities for first entry/exit into a ball.
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Levy Processes with finite variance conditioned to avoid an interval
TL;DR: In this article, the authors studied the question if a Levy process can be conditioned to avoid an interval and, if so, the path behavior of the conditioned process, and they showed that conditioning is possible for Levy processes with finite second moments.
References
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Book
Introductory Lectures on Fluctuations of Lévy Processes with Applications
TL;DR: In this paper, the authors present decompositions of the paths of Levy processes in terms of their local maxima and an understanding of their short-and long-term behaviour.
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Semi-Stable Markov Processes. I
TL;DR: In this article, a real valued random function is called semi-stable if there is a constant > 0 (called the order of the process) such that for every a>O the random functions {x,t } and {a~x,} have the same joint distributions.
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On Lévy processes conditioned to stay positive.
Loïc Chaumont,Ron Doney +1 more
TL;DR: In this paper, the authors construct the law of Levy processes conditioned to stay positive under general hypotheses and obtain a Williams type path decomposition at the minimum of these processes, which is then applied to prove the weak convergence of the law as their initial state tends to 0.
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Recurrent extensions of self-similar Markov processes and Cramér’s condition II
TL;DR: In this paper, a self-similar Markov process X is constructed via its associated entrance law, which can be viewed as X conditioned never to hit 0, and then the process is constructed similarly to the way in which the Brownian excursion measure is constructed through the law of a Bessel(3) process.