Upper estimate of overrunning by Sub&lt;SUB&gt;ϕ&lt;/SUB&gt; (Ω) random process the level specified by continuous function

Vasylyk, Olga; Kozachenko, Yuriy; Yamnenko, Rostyslav

doi:10.1163/156939705323383832

Cited by 10 publications

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“…The theory developed for these processes provides us with powerful techniques and tools suitable not only for asymptotic results, but also for deriving many useful bounds for distributions of these processes. The general theory of ϕ-sub-Gaussian processes and fields is presented in [10,13,19,21,22,26,47,48], simulation methods are given in [23,24,48].…”

Section: Higher-order Heat-type Equations With Random Initial Conditionsmentioning

confidence: 99%

Estimates for Functionals of Solutions to Higher-Order Heat-Type Equations with Random Initial Conditions

et al. 2018

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In the present paper we continue the investigation of solutions to higher-order heat-type equations with random initial conditions, which play the important role in many applied areas. We consider the random initial conditions given by harmonizable ϕ-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema over bounded and unbounded domains for solutions of such equations. The results obtained in the paper hold, in particular, for the case of Gaussian initial condition.

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Section: Higher-order Heat-type Equations With Random Initial Conditionsmentioning

confidence: 99%

Estimates for Functionals of Solutions to Higher-Order Heat-Type Equations with Random Initial Conditions

et al. 2018

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“…These spaces play an important role in extensions of properties of Gaussian and sub-Gaussian processes. Basic results on ϕ-sub-Gaussian processes and fields can be found, for example, in [3,4,8,17].…”

Section: Introductionmentioning

confidence: 99%

Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions

Kozachenko¹,

Orsingher²,

Sakhno³

et al. 2019

Modern Stochastics: Theory and Applications

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In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable ϕ-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema for solutions. We present the examples of processes for which the assumptions of the general result are verified and bounds are written in the explicit form. The main result is also specified for the case of Gaussian initial condition.Keywords Higher-order dispersive equations, random initial conditions, harmonizable processes, sub-Gaussian processes, distribution of sumpremum of solution, entropy methods 2010 MSC 35G10, 35R60, 60G20, 60G60

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“…It is assumed that all processes under consideration are defined on this space. The next theorem follows from Theorem 2.8 of [13] or it could be obtained form Lemma 3.2 of [9]. Theorem 2.1.…”

Section: Definitionmentioning

confidence: 99%

Probability distributions of extremes of self-similar Gaussian random fields

Kozachenko¹,

Makogin²

2014

Journal of Classical Analysis

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We have obtained some upper bounds for the probability distribution of extremes of a selfsimilar Gaussian random field with stationary rectangular increments that are defined on the compact spaces. The probability distributions of extremes for the normalized self-similar Gaussian random fields with stationary rectangular increments defined in R 2 + have been presented. In our work we have used the techniques developed for the self-similar fields and based on the classical series analysis of the maximal probability bounding from below for the Gaussian fields.

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Upper estimate of overrunning by Sub<SUB>ϕ</SUB> (Ω) random process the level specified by continuous function

Cited by 10 publications

References 0 publications

Estimates for Functionals of Solutions to Higher-Order Heat-Type Equations with Random Initial Conditions

Estimates for Functionals of Solutions to Higher-Order Heat-Type Equations with Random Initial Conditions

Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions

Probability distributions of extremes of self-similar Gaussian random fields

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