Counting processes with Bernštein intertimes and random jumps

DOI10.1239/jap/1450802751zbMath1334.60085arXiv1312.1498OpenAlexW2267308078MaRDI QIDQ2794723

Bruno Toaldo, Enzo Orsingher

Publication date: 11 March 2016

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.1498

zbMATH Keywords

subordinatorpoint processesLévy measurerandom jumpsbeta random variableBernštein function

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Sums of independent random variables; random walks (60G50) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (20)

Compositions of Poisson and Gamma processes ⋮ Properties of Poisson processes directed by compound Poisson-gamma subordinators ⋮ A note on Hadamard fractional differential equations with varying coefficients and their applications in probability ⋮ Time-changed space-time fractional Poisson process ⋮ Convoluted Fractional Poisson Process ⋮ Compound Poisson Process with a Poisson Subordinator ⋮ Fractional Poisson processes of order \(k\) and beyond ⋮ Point processes subordinated to compound Poisson processes ⋮ Competing risks and shock models governed by a generalized bivariate Poisson process ⋮ Tempered space fractional negative binomial process ⋮ On spectral properties of stationary random processes connected by a special random time change ⋮ A simple proof of the Lévy-Khintchine formula for subordinators ⋮ Time-inhomogeneous fractional Poisson processes defined by the multistable subordinator ⋮ On martingale characterizations for some generalized space fractional Poisson processes ⋮ Time-changed Poisson processes of order k ⋮ On the long-range dependence of mixed fractional Poisson process ⋮ Recent developments on fractional point processes ⋮ Fractional Poisson process time-changed by Lévy subordinator and its inverse ⋮ On the governing equations for Poisson and Skellam processes time-changed by inverse subordinators ⋮ Skellam and time-changed variants of the generalized fractional counting process

Cites Work

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• Fractional Poisson process
• Fractional Poisson processes and their representation by infinite systems of ordinary differential equations
• Compound Poisson Process with a Poisson Subordinator
• Fractional Gamma and Gamma-Subordinated Processes
• The stability of matter: from atoms to stars
• Fractional Negative Binomial and Polya Processes
• Generalized Gamma measures and shot-noise Cox processes

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