TY - JOUR
T1 - On the stochastic equation L(Z)=L[V(X+Z)] and properties of Mittag–Leffler distributions
AU - Zhang, Zhehao
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/11/15
Y1 - 2019/11/15
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
UR - http://www.scopus.com/inward/record.url?scp=85066987242&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2019.05.003
DO - 10.1016/j.amc.2019.05.003
M3 - Article
AN - SCOPUS:85066987242
SN - 0096-3003
VL - 361
SP - 365
EP - 376
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -