Fluctuation theory for one-sided Lévy processes with a matrix-exponential time horizon

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Fluctuation theory for one-sided Lévy processes with a matrix-exponential time horizon. / Bladt, Mogens; Ivanovs, Jevgenijs.

In: Stochastic Processes and Their Applications, Vol. 142, 2021, p. 105-123.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Bladt, M & Ivanovs, J 2021, 'Fluctuation theory for one-sided Lévy processes with a matrix-exponential time horizon', Stochastic Processes and Their Applications, vol. 142, pp. 105-123. https://doi.org/10.1016/j.spa.2021.08.002

APA

Bladt, M., & Ivanovs, J. (2021). Fluctuation theory for one-sided Lévy processes with a matrix-exponential time horizon. Stochastic Processes and Their Applications, 142, 105-123. https://doi.org/10.1016/j.spa.2021.08.002

Vancouver

Bladt M, Ivanovs J. Fluctuation theory for one-sided Lévy processes with a matrix-exponential time horizon. Stochastic Processes and Their Applications. 2021;142:105-123. https://doi.org/10.1016/j.spa.2021.08.002

Author

Bladt, Mogens ; Ivanovs, Jevgenijs. / Fluctuation theory for one-sided Lévy processes with a matrix-exponential time horizon. In: Stochastic Processes and Their Applications. 2021 ; Vol. 142. pp. 105-123.

Bibtex

@article{d271f98bc0ee418c9aecd9a97f1f88d8,
title = "Fluctuation theory for one-sided L{\'e}vy processes with a matrix-exponential time horizon",
abstract = "There is an abundance of useful fluctuation identities for one-sided L{\'e}vy processes observed up to an independent exponentially distributed time horizon. We show that all the fundamental formulas generalize to time horizons having matrix exponential distributions, and the structure is preserved. Essentially, the positive killing rate is replaced by a matrix with eigenvalues in the right half of the complex plane which, in particular, applies to the positive root of the Laplace exponent and the scale function. Various fundamental properties of thus obtained matrices and functions are established, resulting in an easy to use toolkit. An important application concerns deterministic time horizons which can be well approximated by concentrated matrix exponential distributions. Numerical illustrations are also provided.",
keywords = "Functions of matrices, Rational Laplace transform, Scale function, Wiener–Hopf factorization",
author = "Mogens Bladt and Jevgenijs Ivanovs",
note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",
year = "2021",
doi = "10.1016/j.spa.2021.08.002",
language = "English",
volume = "142",
pages = "105--123",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier BV * North-Holland",

}

RIS

TY - JOUR

T1 - Fluctuation theory for one-sided Lévy processes with a matrix-exponential time horizon

AU - Bladt, Mogens

AU - Ivanovs, Jevgenijs

N1 - Publisher Copyright: © 2021 Elsevier B.V.

PY - 2021

Y1 - 2021

N2 - There is an abundance of useful fluctuation identities for one-sided Lévy processes observed up to an independent exponentially distributed time horizon. We show that all the fundamental formulas generalize to time horizons having matrix exponential distributions, and the structure is preserved. Essentially, the positive killing rate is replaced by a matrix with eigenvalues in the right half of the complex plane which, in particular, applies to the positive root of the Laplace exponent and the scale function. Various fundamental properties of thus obtained matrices and functions are established, resulting in an easy to use toolkit. An important application concerns deterministic time horizons which can be well approximated by concentrated matrix exponential distributions. Numerical illustrations are also provided.

AB - There is an abundance of useful fluctuation identities for one-sided Lévy processes observed up to an independent exponentially distributed time horizon. We show that all the fundamental formulas generalize to time horizons having matrix exponential distributions, and the structure is preserved. Essentially, the positive killing rate is replaced by a matrix with eigenvalues in the right half of the complex plane which, in particular, applies to the positive root of the Laplace exponent and the scale function. Various fundamental properties of thus obtained matrices and functions are established, resulting in an easy to use toolkit. An important application concerns deterministic time horizons which can be well approximated by concentrated matrix exponential distributions. Numerical illustrations are also provided.

KW - Functions of matrices

KW - Rational Laplace transform

KW - Scale function

KW - Wiener–Hopf factorization

UR - http://www.scopus.com/inward/record.url?scp=85114134362&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2021.08.002

DO - 10.1016/j.spa.2021.08.002

M3 - Journal article

AN - SCOPUS:85114134362

VL - 142

SP - 105

EP - 123

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

ER -

ID: 304508420