Loeffen, Ronnie, Patie, Pierre 
ORCID: 0000-0003-4221-0439 and Savov, Mladen
(2018)
Extinction time of non-Markovian self-similar processes, persistence,
annihilation of jumps and the Fréchet distribution.
no., 5 (5).
pp. 1022-1041.
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Abstract
We start by providing an explicit characterization and analytical properties, including the persistence phenomena, of the distribution of the extinction time $\mathbb{T}$ of a class of non-Markovian self-similar stochastic processes with two-sided jumps that we introduce as a stochastic time-change of Markovian self-similar processes. For a suitably chosen time-changed, we observe, for classes with two-sided jumps, the following surprising facts. On the one hand, all the $\mathbb{T}$'s within a class have the same law which we identify in a simple form for all classes and reduces, in the spectrally positive case, to the Fr\'echet distribution. On the other hand, each of its distribution corresponds to the law of an extinction time of a single Markov process without positive jumps, leaving the interpretation that the time-changed has annihilated the effect of positive jumps. The example of the non-Markovian processes associated to L\'evy stable processes is detailed.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | math.PR, math.PR, Primary: 60G18. Secondary: 42A38, 33E50 |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 27 Apr 2020 10:15 |
| Last Modified: | 18 Jan 2023 23:56 |
| DOI: | 10.1007/s10955-019-02279-3 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3081729 |
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