Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)
Wave equation with a stochastic measure
I. M. Bodnarchuk
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Abstract: The Cauchy problem for a wave equation on the line, driven by a general stochastic measure is investigated. The existence, uniqueness and H\"{o}lder regularity of the mild solution are proved.Continuous dependence of the solution on data is established.
Keywords: Stochastic measure, stochastic wave equation, mild solution, H\"{o}lder condition, Besov space.
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