On reflected lévy processes with collapse

Onno J. Boxma; Offer Kella; David Perry

doi:10.1017/jpr.2026.10073

On reflected lévy processes with collapse

Onno J. Boxma
, Offer Kella
, David Perry

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a Lévy process reflected at the origin with additional independent and identically distributed collapses that occur at Poisson epochs, where a collapse is a jump downward to a state which is a random fraction of the state just before the jump. We first study the general case, then specialize to the case where the Lévy process is spectrally positive, and, finally, we specialize further to the two cases where the Lévy process is a Brownian motion and a compound Poisson process with exponential jumps minus a linear slope.

Original language	English
Journal	Journal of Applied Probability
DOIs	https://doi.org/10.1017/jpr.2026.10073
State	Accepted/In press - 2026
Externally published	Yes

Bibliographical note

Publisher Copyright:
© The Author(s), 2026. Published by Cambridge University Press on behalf of Applied Probability Trust.

Keywords

Lindley-style autoregressive recursions
Reflected Lévy process
collapse

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

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10.1017/jpr.2026.10073

Cite this

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title = "On reflected l{\'e}vy processes with collapse",

abstract = "We consider a L{\'e}vy process reflected at the origin with additional independent and identically distributed collapses that occur at Poisson epochs, where a collapse is a jump downward to a state which is a random fraction of the state just before the jump. We first study the general case, then specialize to the case where the L{\'e}vy process is spectrally positive, and, finally, we specialize further to the two cases where the L{\'e}vy process is a Brownian motion and a compound Poisson process with exponential jumps minus a linear slope.",

keywords = "Lindley-style autoregressive recursions, Reflected L{\'e}vy process, collapse",

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doi = "10.1017/jpr.2026.10073",

language = "English",

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T1 - On reflected lévy processes with collapse

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AU - Kella, Offer

AU - Perry, David

PY - 2026

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N2 - We consider a Lévy process reflected at the origin with additional independent and identically distributed collapses that occur at Poisson epochs, where a collapse is a jump downward to a state which is a random fraction of the state just before the jump. We first study the general case, then specialize to the case where the Lévy process is spectrally positive, and, finally, we specialize further to the two cases where the Lévy process is a Brownian motion and a compound Poisson process with exponential jumps minus a linear slope.

AB - We consider a Lévy process reflected at the origin with additional independent and identically distributed collapses that occur at Poisson epochs, where a collapse is a jump downward to a state which is a random fraction of the state just before the jump. We first study the general case, then specialize to the case where the Lévy process is spectrally positive, and, finally, we specialize further to the two cases where the Lévy process is a Brownian motion and a compound Poisson process with exponential jumps minus a linear slope.

KW - Lindley-style autoregressive recursions

KW - Reflected Lévy process

KW - collapse

UR - https://www.scopus.com/pages/publications/105033104756

U2 - 10.1017/jpr.2026.10073

DO - 10.1017/jpr.2026.10073

M3 - Article

AN - SCOPUS:105033104756

SN - 0021-9002

JO - Journal of Applied Probability

JF - Journal of Applied Probability

ER -

On reflected lévy processes with collapse

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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