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

Abstract

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 - 39

Language of the article: English

Author Biographies

O. D. Kollie, Taras Shevchenko National University of Kyiv
Student
R. E. Yamnenko, Taras Shevchenko National University of Kyiv
Department of Probability Theory, Statistics and Actuarial Mathematics, Associated Professor

References

BULDYGIN, V.V. and KOZACHENKO, Yu.V. (2000), Metric characterization of random variables and random processes, AMS, Providence RI.

VASYLYK, O., KOZACHENKO, Yu. and YAMNENKO R. (2008), φ-subgaussovi vypadkovi protsesy: monographiya, Kyiv: Vydavnycho-Poligrafichnyi Tsentr, Kyivskyi Universytet, 231p.

VASYLYK, O. and YAMNENKO R. (2007), ”Random Process from the Class V (φ, ψ): Exceeding a Curve“, Theory of Stochastic Processes, Vol. 13(29), n.4, .pp.219–232.

How to Cite
Kollie, O. D., & Yamnenko, R. E. (1). Alternative estimate of curve exceeding probability of sub-Gaussian random process. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, (1-2), 37-39. https://doi.org/10.17721/1812-5409.2020/1-2.5
Section
Algebra, Geometry and Probability Theory