Journal article

Wave Equation With A Coloured Stable Noise

Year:

2017

Published in:

Random Operators and Stochastic Equations
Stochastic partial differential equation
wave equation
Kirchhoff’s formula
harmonizable fractional stable field
LePage representation
Hölder continuity

We define a random measure generated by a real anisotropic harmonizable fractional stable field ZHZH with stability parameter α∈(1,2)α∈(1,2) and Hurst index H∈(12,1)H∈(12,1) and prove that the measure is σ-additive in probability. An integral with respect to this measure is constructed, which enables us to consider a wave equation in R3ℝ3 with a random source generated by ZHZH. We show that the solution to this equation, given by Kirchhoff’s formula, has a modification, which is Hölder continuous of any order up to (3H−1)∧1(3⁢H-1)∧1. In the case where H∈(23,1)H∈(23,1), we show further that the modification is absolutely continuous.

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Publisher: Statistical Inference for Stochastic Processes

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2011
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Rate Of Convergence Of Euler Approximations Of Solution To Mixed Stochastic Differential Equation Involving Brownian Motion And Fractional Brownian Motion

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Publisher: Statistics & Probability Letters

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2021
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Publisher: Journal of Theoretical Probability

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2014
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Fractional Brownian Motion In A Nutshell

Publisher: arxiv

Authors: Georgiy Shevchenko

2007
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Publisher: Theory of Probability & Its Applications

Authors: Georgiy Shevchenko, Yulia Mishura

2018
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Publisher: arxiv

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Tail Measures And Regular Variation

Publisher: Electronic Journal of Probability

Authors: Georgiy Shevchenko, Martin Bladt, Enkelejd Hashorva