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Continuous-state branching processes with collisions: first passage times and dualityFoucart, Clément ; Vidmar, Matija, 1988-We introduce a class of one-dimensional positive Markov processes generalizing continuous-state branching processes (CBs), by taking into account a phenomenon of random collisions. Besides branching, ... characterized by a general mechanism ▫$\Psi$▫, at a constant rate in time two particles are sampled uniformly in the population, collide and leave a mass of particles governed by a (sub)critical mechanism ▫$\Sigma$▫. Such CB processes with collisions (CBCs) are shown to be the only Feller processes without negative jumps satisfying a Laplace duality relationship with one-dimensional diffusions on the half-line. This generalizes the duality observed for logistic CBs by Foucart (2019). Via time-change, CBCs are also related to an auxiliary class of Markov processes, called CB processes with spectrally positive migration (CBMs), recently introduced by Vidmar (2022). We find necessary and sufficient conditions for the boundaries ▫$0$▫ or ▫$\infty$▫ to be attracting and for a limiting distribution to exist. The Laplace transform of the latter is provided. Under the assumption that the CBC process does not explode, the Laplace transforms of the first passage times below arbitrary levels are represented with the help of the solution of a secondorder differential equation, whose coefficients express in terms of the Lévy–Khintchine functions ▫$\Sigma$▫ and ▫$\Psi$▫. Sufficient conditions for non-explosion are given.Source: Stochastic Processes and their Applications. - ISSN 0304-4149 (Vol. 167, [article no.] 104230, Jan. 2024, 35 str.)Type of material - article, component part ; adult, seriousPublish date - 2024Language - englishCOBISS.SI-ID - 170650115
Author | Foucart, Clément ; Vidmar, Matija, 1988- |
Title | Continuous-state branching processes with collisions: first passage times and duality |
Publication date | 2023-10-01 |
COBISS.SI-ID | 170650115 |
Publication version in repository | Publisher's version |
Publication licence | Creative Commons Attribution 4.0 International |
Embargo | Immediate publication for public |
Project(s) from which the publication was funded
Title | Acronym | Project ID | Funder |
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Časi prvih prehodov eno-stranskih procesov Markova | N1-0174-2021 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
|
Matematična fizika | P1-0402-2019 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
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https://www.sciencedirect.com/science/article/pii/S0304414923002028 |
https://repozitorij.uni-lj.si/IzpisGradiva.php?id=153109 |
source: Stochastic Processes and their Applications. - ISSN 0304-4149 (Vol. 167, [article no.] 104230, Jan. 2024, 35 str.)
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Foucart, Clément | |
Vidmar, Matija, 1988- | 37670 |
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