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Theory of Probability and Mathematical Statistics



Wave equation in three-dimensional space driven by a general stochastic measure

I. M. Bodnarchuk, V. M. Radchenko

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Abstract: The Cauchy problem for a wave equation in three-dimensional space driven by a general stochastic measure is investigated. The existence and uniqueness of the mild solution are proved. Hölder regularity of its paths in time and spatial variables is obtained.

Keywords: Stochastic measure, stochastic wave equation, mild solution, Holder condition, Besov space.

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