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

Zhehao Zhang

Applied Mathematics and Computation, 2019, vol. 361, issue C, 365-376

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; Mittag–Leffler distribution; Hypergeometric functions; Laplace transform; Mellin transform (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:361:y:2019:i:c:p:365-376

DOI: 10.1016/j.amc.2019.05.003

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