Heat equation and wave equation with general stochastic measures
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- Radchenko, V.N. Ukr Math J (2008) 60: 1968. doi:10.1007/s11253-009-0184-2
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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.