Estimates for Distributions of Suprema of Spherical Random Fields

Sakhno, Lyudmyla

doi:10.19139/soic-2310-5070-1705

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…Theorem 1.2 with a particular metric space (T, d) has been applied in Hopkalo and Sakhno (2021); Kozachenko et al (2020); Sakhno (2023b) for studying solutions to partial differential equations with random initial condition, in Sakhno (2023a) for evaluation of suprema of spherical random fields, in Kozachenko and Olenko (2016) for developing uniform approximation schemes for ϕ-sub-Gaussian processes. This theorem allows to calculate the bounds for the distribution of suprema in the closed form.…”

Section: Introductionmentioning

confidence: 99%

Bounds for the Tail Distributions of Suprema of Sub-Gaussian Type Random Fields

Hopkalo,

Sakhno,

Vasylyk

2023

AJS

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The paper presents bounds for the distributions of suprema for particular classes of ϕ-sub-Gaussian random fields. Results stated depend on representations of bounds for increments of the fields in different metrics. Several examples of applications are provided to illustrate the results, in particular, to random fields related to stochastic partial differential equations and partial differential equations with random initial conditions.

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Section: Introductionmentioning

confidence: 99%

Bounds for the Tail Distributions of Suprema of Sub-Gaussian Type Random Fields

Hopkalo,

Sakhno,

Vasylyk

2023

AJS

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“…Applying entropy methods for stochastic processes from these classes allows one to investigate the behavior of their extrema, to derive estimates for various functionals of such processes and random fields, to treat their sample paths properties, see, for example, Dozzi, Kozachenko, Mishura, and Ralchenko (2018); Yamnenko (2017); Hopkalo and Sakhno (2021); Sakhno (2022).…”

Section: Introductionmentioning

confidence: 99%

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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“…The main theory for the spaces of ϕ-sub-Gaussian random variables and stochastic processes was presented in [4,7,16] followed by numerous further studies. Various classes of ϕ-sub-Gaussian processes and fields were studied, in particular, in [3,9,13,14,15,17].…”

Section: Introductionmentioning

confidence: 99%

Properties of solutions to linear KdV equations with φ-sub-Gaussian initial conditions

Hopkalo

Sakhno

Vasylyk

2022

BKNUPhM

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In this paper, there are studied sample paths properties of stochastic processes representing solutions (in L_2(Ω) sense) to the linear Korteweg–de Vries equation (called also the Airy equation) with random initial conditions given by φ-sub-Gaussian stationary processes. The main results are the bounds for the distributions of the suprema for such stochastic processes considered over bounded domains. Also, there are presented some examples to illustrate the results of the study.

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Estimates for Distributions of Suprema of Spherical Random Fields

Abstract: Bounds for distributions of suprema of $\varphi$-sub-Gaussian random fields defined over the $N$-dimensional unit sphere are stated. Applications of the results to the spherical fractional Brownian motion, isotropic Gaussian fields and some other models are presented.

Cited by 5 publications

References 21 publications

Bounds for the Tail Distributions of Suprema of Sub-Gaussian Type Random Fields

Bounds for the Tail Distributions of Suprema of Sub-Gaussian Type Random Fields

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

Properties of solutions to linear KdV equations with φ-sub-Gaussian initial conditions

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