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 pro...
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| Format: | Article |
| Language: | English |
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Austrian Statistical Society
2023-08-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | https://www.ajs.or.at/index.php/ajs/article/view/1761 |
| _version_ | 1797735768221810688 |
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| author | Dmytro Tykhonenko Rostyslav Yamnenko |
| author_facet | Dmytro Tykhonenko Rostyslav Yamnenko |
| author_sort | Dmytro Tykhonenko |
| collection | DOAJ |
| description |
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.
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| first_indexed | 2024-03-12T13:03:52Z |
| format | Article |
| id | doaj.art-db16ddcdd9cb4b74bf9fac17d7ae739d |
| institution | Directory Open Access Journal |
| issn | 1026-597X |
| language | English |
| last_indexed | 2024-03-12T13:03:52Z |
| publishDate | 2023-08-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj.art-db16ddcdd9cb4b74bf9fac17d7ae739d2023-08-28T18:34:36ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2023-08-0152SI10.17713/ajs.v52iSI.1761Supremum Distribution of Weighted Sum of Random Processes from Orlicz Spaces of Exponential Type with Continuous DeviationDmytro TykhonenkoRostyslav Yamnenko 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. https://www.ajs.or.at/index.php/ajs/article/view/1761 |
| spellingShingle | Dmytro Tykhonenko Rostyslav Yamnenko Supremum Distribution of Weighted Sum of Random Processes from Orlicz Spaces of Exponential Type with Continuous Deviation Austrian Journal of Statistics |
| title | Supremum Distribution of Weighted Sum of Random Processes from Orlicz Spaces of Exponential Type with Continuous Deviation |
| title_full | Supremum Distribution of Weighted Sum of Random Processes from Orlicz Spaces of Exponential Type with Continuous Deviation |
| title_fullStr | Supremum Distribution of Weighted Sum of Random Processes from Orlicz Spaces of Exponential Type with Continuous Deviation |
| title_full_unstemmed | Supremum Distribution of Weighted Sum of Random Processes from Orlicz Spaces of Exponential Type with Continuous Deviation |
| title_short | Supremum Distribution of Weighted Sum of Random Processes from Orlicz Spaces of Exponential Type with Continuous Deviation |
| title_sort | supremum distribution of weighted sum of random processes from orlicz spaces of exponential type with continuous deviation |
| url | https://www.ajs.or.at/index.php/ajs/article/view/1761 |
| work_keys_str_mv | AT dmytrotykhonenko supremumdistributionofweightedsumofrandomprocessesfromorliczspacesofexponentialtypewithcontinuousdeviation AT rostyslavyamnenko supremumdistributionofweightedsumofrandomprocessesfromorliczspacesofexponentialtypewithcontinuousdeviation |