We consider the heat equation and wave equation with constant coefficients that contain a term given by an integral with respect to a random measure. Only the condition of sigma-additivity in probability is imposed on the random measure. Solutions of these equations are presented. For each equation, we prove that its solutions coincide under certain additional conditions.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1675 – 1685, December, 2008.
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Radchenko, V.N. Heat equation and wave equation with general stochastic measures. Ukr Math J 60, 1968–1981 (2008). https://doi.org/10.1007/s11253-009-0184-2
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DOI: https://doi.org/10.1007/s11253-009-0184-2