Weak convergence of renewal shot noise processes in the case of slowly varying normalization

DOI10.1016/j.spl.2016.03.015zbMath1337.60021arXiv1507.02526OpenAlexW2963186811MaRDI QIDQ277276

Alexander Marynych, Zakhar Kabluchko, Aleksander M. Iksanov

Publication date: 4 May 2016

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.02526

zbMATH Keywords

weak convergenceBrownian motionGaussian processesrandom walkrenewal shot noise processesslowly varying functions

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Brownian motion (60J65) Rate of growth of functions, orders of infinity, slowly varying functions (26A12) Renewal theory (60K05)

Related Items (5)

A functional limit theorem for random processes with immigration in the case of heavy tails ⋮ Weak convergence of renewal shot noise processes in the case of slowly varying normalization ⋮ Fractionally integrated inverse stable subordinators ⋮ A functional limit theorem for general shot noise processes ⋮ Stationary limits of shot noise processes

Cites Work

• Weak convergence of renewal shot noise processes in the case of slowly varying normalization
• Moment convergence of first-passage times in renewal theory
• Mesoscopic fluctuations of the zeta zeros
• Invariance principles for renewal processes
• Functional limit theorems for renewal shot noise processes with increasing response functions
• On a stochastic difference equation and a representation of non–negative infinitely divisible random variables
• Stopped Random Walks
• Weak Convergence of Finite-Dimensional Distributions of the Number of Empty Boxes in the Bernoulli Sieve
• Gaussian fluctuations of Young diagrams under the Plancherel measure
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