Stationary limits of shot noise processes

Verovkin, G.; Marynych, A.

doi:10.1090/tpms/1112

Stationary limits of shot noise processes

Authors: G. K. Verovkin and A. V. Marynych
Translated by: S. V. Kvasko
Journal: Theor. Probability and Math. Statist. 101 (2020), 67-83
MSC (2020): Primary 60F05; Secondary 60K05
DOI: https://doi.org/10.1090/tpms/1112
Published electronically: January 5, 2021
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Abstract: The weak convergence of centered shot noise processes to a stationary $\mathcal {L}_2$-process is proved under the assumption that the response function is mean square integrable and variance of the step of the underlying random walk is finite. Properties of the limiting stationary process are studied.

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