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Implicit renewal theory for exponential functionals of Lévy processes

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Implicit renewal theory for exponential functionals of Lévy processes. / Arista, Jonas; Rivero, Víctor.
In: Stochastic Processes and their Applications, Vol. 163, 30.09.2023, p. 262-287.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Arista, J & Rivero, V 2023, 'Implicit renewal theory for exponential functionals of Lévy processes', Stochastic Processes and their Applications, vol. 163, pp. 262-287. https://doi.org/10.1016/j.spa.2023.06.004

APA

Arista, J., & Rivero, V. (2023). Implicit renewal theory for exponential functionals of Lévy processes. Stochastic Processes and their Applications, 163, 262-287. https://doi.org/10.1016/j.spa.2023.06.004

Vancouver

Arista J, Rivero V. Implicit renewal theory for exponential functionals of Lévy processes. Stochastic Processes and their Applications. 2023 Sept 30;163:262-287. Epub 2023 Jun 30. doi: 10.1016/j.spa.2023.06.004

Author

Arista, Jonas ; Rivero, Víctor. / Implicit renewal theory for exponential functionals of Lévy processes. In: Stochastic Processes and their Applications. 2023 ; Vol. 163. pp. 262-287.

Bibtex

@article{400cf970ed9a4ead92ae9c81e01e261c,
title = "Implicit renewal theory for exponential functionals of L{\'e}vy processes",
abstract = "We establish a new integral equation for the probability density of the exponential functional of a L{\'e}vy process and provide a three-term (Wiener–Hopf type) factorisation of its law. We explain how these results complement the techniques used in the study of exponential functionals and, in some cases, provide quick proofs of known results and derive new ones. We explain how the factors appearing in the three-term factorisation determine the local and asymptotic behaviour of the law of the exponential functional. We describe the behaviour of the tail distribution at infinity and of the distribution at zero under some mild assumptions.",
author = "Jonas Arista and V{\'i}ctor Rivero",
year = "2023",
month = sep,
day = "30",
doi = "10.1016/j.spa.2023.06.004",
language = "English",
volume = "163",
pages = "262--287",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Implicit renewal theory for exponential functionals of Lévy processes

AU - Arista, Jonas

AU - Rivero, Víctor

PY - 2023/9/30

Y1 - 2023/9/30

N2 - We establish a new integral equation for the probability density of the exponential functional of a Lévy process and provide a three-term (Wiener–Hopf type) factorisation of its law. We explain how these results complement the techniques used in the study of exponential functionals and, in some cases, provide quick proofs of known results and derive new ones. We explain how the factors appearing in the three-term factorisation determine the local and asymptotic behaviour of the law of the exponential functional. We describe the behaviour of the tail distribution at infinity and of the distribution at zero under some mild assumptions.

AB - We establish a new integral equation for the probability density of the exponential functional of a Lévy process and provide a three-term (Wiener–Hopf type) factorisation of its law. We explain how these results complement the techniques used in the study of exponential functionals and, in some cases, provide quick proofs of known results and derive new ones. We explain how the factors appearing in the three-term factorisation determine the local and asymptotic behaviour of the law of the exponential functional. We describe the behaviour of the tail distribution at infinity and of the distribution at zero under some mild assumptions.

U2 - 10.1016/j.spa.2023.06.004

DO - 10.1016/j.spa.2023.06.004

M3 - Journal article

VL - 163

SP - 262

EP - 287

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

ER -