Properties of strictly \(\varphi \)-sub-Gaussian quasi-shot-noise processes. (English. Ukrainian original) Zbl 1455.60054

Theory Probab. Math. Stat. 101, 51-65 (2020); translation from Teor. Jmovirn. Mat. Stat. 101, 49-62 (2019).
Summary: Properties of \(\varphi \)-sub-Gaussian quasi-shot-noise processes \[ X(t)=\int_{-\infty }^{+\infty }g(t,u)\,d\xi (u), \quad t\in \mathbf{R},\] 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.


60G07 General theory of stochastic processes
60K25 Queueing theory (aspects of probability theory)
60G15 Gaussian processes
60G99 Stochastic processes
Full Text: DOI


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