On the stochastic equation L(Z)=L[V(X+Z)] and properties of Mittag–Leffler distributions

Zhehao Zhang

doi:10.1016/j.amc.2019.05.003

On the stochastic equation L(Z)=L[V(X+Z)] and properties of Mittag–Leffler distributions

Zhehao Zhang

Department of Financial and Actuarial Mathematics

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

1 Citation (Scopus)

Abstract

The stochastic equation Z=dV(X+Z), where V, X and Z are independent, has a wide range of applications in finance, insurance, telecommunications and time series analysis. Dufresne[8,9] solves for some specific cases of this equation by the algebraic properties of beta and gamma distributions. This paper aims to generalise Dufresne's results to beta and Mittag–Leffler distributions and solve for new specific distributions of Z.

Original language	English
Pages (from-to)	365-376
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	361
DOIs	https://doi.org/10.1016/j.amc.2019.05.003
Publication status	Published - 15 Nov 2019

Keywords

Beta distribution
Hypergeometric functions
Laplace transform
Mellin transform
Mittag–Leffler distribution

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10.1016/j.amc.2019.05.003

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title = "On the stochastic equation L(Z)=L[V(X+Z)] and properties of Mittag–Leffler distributions",

abstract = "The stochastic equation Z=dV(X+Z), where V, X and Z are independent, has a wide range of applications in finance, insurance, telecommunications and time series analysis. Dufresne[8,9] solves for some specific cases of this equation by the algebraic properties of beta and gamma distributions. This paper aims to generalise Dufresne's results to beta and Mittag–Leffler distributions and solve for new specific distributions of Z.",

keywords = "Beta distribution, Hypergeometric functions, Laplace transform, Mellin transform, Mittag–Leffler distribution",

author = "Zhehao Zhang",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

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N2 - The stochastic equation Z=dV(X+Z), where V, X and Z are independent, has a wide range of applications in finance, insurance, telecommunications and time series analysis. Dufresne[8,9] solves for some specific cases of this equation by the algebraic properties of beta and gamma distributions. This paper aims to generalise Dufresne's results to beta and Mittag–Leffler distributions and solve for new specific distributions of Z.

AB - The stochastic equation Z=dV(X+Z), where V, X and Z are independent, has a wide range of applications in finance, insurance, telecommunications and time series analysis. Dufresne[8,9] solves for some specific cases of this equation by the algebraic properties of beta and gamma distributions. This paper aims to generalise Dufresne's results to beta and Mittag–Leffler distributions and solve for new specific distributions of Z.

KW - Beta distribution

KW - Hypergeometric functions

KW - Laplace transform

KW - Mellin transform

KW - Mittag–Leffler distribution

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EP - 376

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

On the stochastic equation L(Z)=L[V(X+Z)] and properties of Mittag–Leffler distributions

Abstract

Keywords

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