TY - JOUR
AU - Kollie, O. D.
AU - Yamnenko, R. E.
PY - 2020/03/09
Y2 - 2023/05/30
TI - Alternative estimate of curve exceeding probability of sub-Gaussian random process
JF - Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics
JA - BTSNUKPhM
VL -
IS - 1-2
SE - Algebra, Geometry and Probability Theory
DO - 10.17721/1812-5409.2020/1-2.5
UR - https://bphm.knu.ua/index.php/bphm/article/view/134
SP - 37-39
AB - <p>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.</p><p><em><strong><span lang="EN-US">Key words</span></strong></em><span lang="EN-US">: </span>sub-Gaussian process, metric entropy, supremum distribution, trajectory of random process.</p><p><em><strong><span lang="EN-US">Pages of the article in the issue</span></strong></em><span lang="EN-US">: 37 - 39</span></p><p><strong><em><span lang="EN-US">Language of the article</span></em></strong><span lang="EN-US">: English</span></p>
ER -