Theory of Probability and Mathematical Statistics
Wave equation in a plane driven by a general stochastic measure
I. M. Bodnarchuk, V. M. Radchenko
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Abstract: The Cauchy problem for a wave equation on the plain, driven by a general stochastic measure is investigated. The existence and uniqueness of the mild solution are proved. Holder regularity of its paths in time and spatial variables is obtained. Continuous dependence of the solution on data is established.
Keywords: Stochastic measure, stochastic wave equation, mild solution, Holder condition, Besov space.
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