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

摘要

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.