Shot Noise Distributions and Selfdecomposability

DOI10.1081/SAP-120020428zbMath1042.60026arXivmath/0111069MaRDI QIDQ4804872

Zbigniew J. Jurek, Aleksander M. Iksanov

Publication date: 28 April 2003

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0111069

zbMATH Keywords

subordinationregular variationrandom integral representationshot noise processes

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) General theory of stochastic processes (60G07) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Renewal theory (60K05)

Related Items (7)

A new factorization property of the selfdecomposable probability measures. ⋮ Networks of \(\cdot /\mathrm{G}/\infty \) queues with shot-noise-driven arrival intensities ⋮ Nonparametric estimation of Mark's distribution of an exponential shot-noise process ⋮ Infinite divisibility of infinite sums of lower records: a simple proof ⋮ Renormalization group of and convergence to the LISDLG process ⋮ On perpetuities with gamma-like tails ⋮ Shot-noise queueing models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Mittag-Leffler functions and related distributions
• Loud shot noise
• Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type
• On a continuous analogue of the stochastic difference equation \(X_ n\) = rho X//(n-1) + \(B_ n\).
• Generalized gamma convolutions and related classes of distributions and densities
• Unimodality of infinitely divisible distribution functions of class L
• On the self-decomposability of the half-Cauchy distribution
• On geometric-stable laws, a related property of stable processes, and stable densities of exponent one
• A note on gamma random variables and Dirichlet series
• On a stochastic difference equation and a representation of non–negative infinitely divisible random variables
• An integral representation for selfdecomposable banach space valued random variables
• Extremal properties of shot noise processes
• Infinite Divisibility and Variance Mixtures of the Normal Distribution
• Subordination and self-decomposability

This page was built for publication: Shot Noise Distributions and Selfdecomposability