Alternative estimate of curve exceeding probability of sub-Gaussian random process

Kollie, O. D., Yamnenko, R. E. (2020). Alternative estimate of curve exceeding probability of sub-Gaussian random process. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(1), 37–39. https://doi.org/10.17721/1812-5409.2020/1-2.5

Investigation of sub-gaussian random processes are of special interest since obtained results can be applied to Gaussian processes. In this article the properties of trajectories of a sub-Gaussian process drifted by a curve a studied. The following functionals of extremal type from stochastic process are studied: $\sup_{t\in B}(X(t)-f(t))$, $\inf{t\in B}(X(t)-f(t))$ and $\sup_{t\in B}|X(t)-f(t)|$. An alternative estimate of exceeding by sub-Gaussian process a level, given by a continuous linear curve is obtained. The research is based on the results obtained in the work \cite{yamnenko_vasylyk_TSP_2007}. The results can be applied to such problems of queuing theory and financial mathematics as an estimation of buffer overflow probability and bankruptcy probability.Key words: sub-Gaussian process, metric entropy, supremum distribution, trajectory of random process.Pages of the article in the issue: 37 - 39Language of the article: English