# Estimation of probability of exceeding a curve by a strictly ?-sub-Gaussian quasi shot noise process

## DOI:

https://doi.org/10.17721/1812-5409.2020/3.5## Abstract

In this paper, we continue to study the properties of a separable strictly ?-sub-Gaussian quasi shot noise process $X(t) = \int_{-\infty}^{+\infty} g(t,u) d\xi(u), t\in\R$, generated by the response function g and the strictly ?-sub-Gaussian process ? = (?(t), t ? R) with uncorrelated increments, such that E(?(t)??(s))^2 = t?s, t>s ? R. We consider the problem of estimating the probability of exceeding some level by such a process on the interval [a;b], a,b ? R. The level is given by a continuous function f = {f(t), t ? [a;b]}, which satisfies some given conditions. In order to solve this problem, we apply the theorems obtained for random processes from a class V (?, ?), which generalizes the class of ?-sub-Gaussian processes. As a result, several estimates for probability of exceeding the curve f by sample pathes of a separable strictly ?-sub-Gaussian quasi shot noise process are obtained. Such estimates can be used in the study of shot noise processes that arise in the problems of financial mathematics, telecommunication networks theory, and other applications.

* Key words*: shot noise processes, ?-sub-Gaussian processes.

* Pages of the article in the issue*: 49 - 56

** Language of the article**: Ukrainian

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*Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics*, (3), 49–56. https://doi.org/10.17721/1812-5409.2020/3.5

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