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Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



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

O. I. Vasylyk

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Abstract: In this paper, there are studied properties of a strictly $\varphi$-sub-Gaussian quasi shot noise process $ X(t)=\int_{-\infty}^{+\infty}g(t,u)d\xi(u),$ $t\in\R$, generated by the process $\xi$ and the response function~$g$. There are obtained conditions, under which such random processes belong to some weighted spaces of continuous functions. Estimates for distributions of suprema of strictly $\varphi$-sub-Gaussian quasi shot noise processes are derived.

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