Supremum Distribution of Weighted Sum of Random Processes from Orlicz Spaces of Exponential Type with Continuous Deviation
The paper studies distribution of sum of random processes from Orlicz spaces of exponential type weighted by continuous functions, in particular, processes from spaces Subϕ (Ω), SSubϕ (Ω) and class V (ϕ, ψ) are considered. Such spaces and classes of random variables and corresponding stochastic processes provide generalizations of Gaussian and sub-Gaussian random variables and processes and are important for various applications, for example, in queuing theory and financial mathematics. We derive the estimates for the distribution of supremum of weighted sum of such processes deviated by a continuous monotone function using the entropy method. As examples, weighted sum of Wiener and weighted sum of fractional Brownian motion processes with different Hurst indices from classes V (ϕ, ψ) are considered. Corresponding estimates of the probability of exceeding by trajectories of such weighted sums a positive level determined by a linear function are obtained. In the insurance risk theory, such a
problem arises during estimating a ruin probability of the corresponding risk process with a constant premium income, and in the communications theory, it appears for the buffer overflow probability for a single server with a constant service rate.
How to Cite
Copyright (c) 2023 Dmytro Tykhonenko, Rostyslav Yamnenko
This work is licensed under a Creative Commons Attribution 3.0 Unported License.
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.