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

Authors

DOI:

https://doi.org/10.17721/1812-5409.2020/1-2.5

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.

No 1-2 (2020)

Downloads

How to Cite

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. Physical and Mathematical Sciences, (1-2), 37–39. https://doi.org/10.17721/1812-5409.2020/1-2.5

Issue

No. 1-2 (2020)

Section

Algebra, Geometry and Probability Theory

License

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).