Ukrainian Mathematical Journal

, Volume 60, Issue 12, pp 1968-1981

First online:

Heat equation and wave equation with general stochastic measures

  • V. N. RadchenkoAffiliated withShevchenko Kyiv National University

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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.