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

Alexander Iksanov, Zakhar Kabluchko and Alexander Marynych

Statistics & Probability Letters, 2016, vol. 114, issue C, 67-77

Abstract: We investigate weak convergence of finite-dimensional distributions of a renewal shot noise process (Y(t))t≥0 with deterministic response function h and the shots occurring at the times 0=S02 we use a strong approximation argument to show that the random fluctuations of Y(s) occur on the scale s=t+g(t,u) for u∈[0,1], as t→∞, and, on the level of finite-dimensional distributions, are well approximated by the sum of a Brownian motion and a Gaussian process with independent values (the two processes being independent). The scaling function g above depends on the slowly varying factor of h. If, for instance, limt→∞t1/2h(t)∈(0,∞), then g(t,u)=tu.

Keywords: Gaussian process with independent values; Renewal shot noise process; Weak convergence of finite-dimensional distributions (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2016.03.015

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