Local properties of a multifractional stable field

Shevchenko, Georgiy

doi:10.1090/s0094-9000-2013-00882-5

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Real Anisotropic Harmonizable Fractional Stable Field1

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Cited by 3 publications

(1 citation statement)

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“…for technical reasons we will restrict ourselves to the case α ∈ (1, 2), H ∈ (1/2, 1). The properties of Z H were established in [8], in [21] its multifractional was defined and investigated. In particular, it was proved in the cited articles that this field has a modification, which is locally Hölder continuous of any order β ∈ (0, H).…”

Section: Real Anisotropic Harmonizable Fractional Stable Fieldmentioning

confidence: 99%

Wave equation with a coloured stable noise

Pryhara

Shevchenko

2017

Random Operators and Stochastic Equations

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Abstract. We define a random measure generated by a real anisotropic harmonizable fractional stable field Z H with stability parameter α ∈ (1, 2) and Hurst index H ∈ (1/2, 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 R 3 with a random source generated by Z H . 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. In the case where H ∈ (2/3, 1), we show further that the modification is absolutely continuous.

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Section: Real Anisotropic Harmonizable Fractional Stable Fieldmentioning

confidence: 99%