Application of $$\varphi$$ -Sub-Gaussian Random Processes in Queueing Theory

Kozachenko, Yuriy; Yamnenko, Rostyslav

doi:10.1007/978-3-319-03512-3_2

Cited by 3 publications

(5 citation statements)

References 8 publications

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“…Here we generalize results obtained by Kozachenko and Yamnenko (2014) for weighted sum of independent processes from such classes. Our main interest is focused on studying the distribution of the following functionals…”

Section: Introductionsupporting

confidence: 74%

“…. (10) Some details are omitted here since the same derivation can be found also in Kozachenko and Yamnenko (2014).…”

Section: Resultsmentioning

confidence: 99%

“…Section 2 is devoted to the general theory of random variables and processes from Orlicz spaces of exponential type and based on the works Buldygin and Kozachenko (2000); Kozachenko and Vasylyk (2001); Vasylyk et al (2008); Vasylyk and Yamnenko (2007); Yamnenko, Kozachenko, and Bushmitch (2014). Section 3 contains a generalization of results from the papers Kozachenko and Yamnenko (2014) and the last section contains applications to generalized Wiener and FBM processes from classes V (ϕ, ψ).…”

Section: Introductionmentioning

confidence: 99%

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Supremum Distribution of Weighted Sum of Random Processes from Orlicz Spaces of Exponential Type with Continuous Deviation

Tykhonenko,

Yamnenko

2023

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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 aproblem 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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Section: Introductionsupporting

confidence: 74%

“…. (10) Some details are omitted here since the same derivation can be found also in Kozachenko and Yamnenko (2014).…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Supremum Distribution of Weighted Sum of Random Processes from Orlicz Spaces of Exponential Type with Continuous Deviation

Tykhonenko,

Yamnenko

2023

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“…It extends a series of papers [4,5,12,13,14] studying probabilities of exceeding by such processes a level specified by a given function in C(T) spaces. Such problems find an application in queuing and risk theories, for example, for estimating the ruin probability or buffer overflow probability in a model with ϕ-sub-Gaussian input process.…”

Section: Introductionmentioning

confidence: 94%

“…General theory and various applications of sub-Gaussian, ϕ-sub-Gaussian, and strictly ϕ-sub-Gaussian random variables and processes can be found in the book of Buldygin and Kozachenko [1] and in the papers [2,4,5,7,8,9,12,13,14].…”

Section: Introductionmentioning

confidence: 99%