Properties of strictly 𝜑-sub-Gaussian quasi-shot-noise processes

Vasylyk, O.

doi:10.1090/tpms/1111

Properties of strictly $\varphi$-sub-Gaussian quasi-shot-noise processes

Author: O. I. Vasylyk
Translated by: N. N. Semenov
Journal: Theor. Probability and Math. Statist. 101 (2020), 51-65
MSC (2020): Primary 60G07, 60G17, 60F10, 60H05, 60K40
DOI: https://doi.org/10.1090/tpms/1111
Published electronically: January 5, 2021
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Abstract: Properties of $\varphi$-sub-Gaussian quasi-shot-noise processes \begin{equation*} X(t)=\int _{-\infty }^{+\infty }g(t,u) d\xi (u), \qquad t\in \mathbf {R}, \end{equation*} generated by a stochastic process $\xi$ and response function $g$ are studied in the paper. Sufficient conditions for quasi-shot-noise processes to belong to weighted spaces of continuous functions are obtained. Bounds for the distributions of supremums of strictly $\varphi$-sub-Gaussian quasi-shot-noise processes are established.

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