Theory of Probability and Mathematical Statistics
Mild solution of a parabolic equation driven by a sigma-finite stochastic measure
O. O. Vertsimakha, V. M. Radchenko
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Abstract: The stochastic parabolic equation on [0,T]xR driven by sigma-finite stochastic measure is investigated. For the integrator we assume sigma-additivity in probability on bounded Borel sets only. Existence and uniqueness of the mild solution is established. Holder continuity of the solution is proved. Thus, we get a generalisation of results obtained for usual stochastic measures in previous papers.
Keywords: Stochastic measure, sigma-finite stochastic measure, stochastic parabolic equation, mild solution, Holder continuity
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