Mild solution of the parabolic equation driven by a \sigma-finite stochastic measure

Stochastic parabolic equation driven by a \sigma -finite stochastic measure in the interval [0,T]\times \mathbb{R} is studied. The only condition imposed on the stochastic integrator is its \sigma -additivity in probability on bounded Borel sets. The existence, uniqueness, and Hölder continuity of a...

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Bibliographic Details
Published in:Theory of probability and mathematical statistics 2018, Vol.97, p.17-32
Main Authors: Vertsimakha, O. O., Radchenko, V. M.
Format: Article
Language:English
Online Access:Get full text
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Summary:Stochastic parabolic equation driven by a \sigma -finite stochastic measure in the interval [0,T]\times \mathbb{R} is studied. The only condition imposed on the stochastic integrator is its \sigma -additivity in probability on bounded Borel sets. The existence, uniqueness, and Hölder continuity of a mild solution are proved. These results generalize those known earlier for usual stochastic measures.
ISSN:0094-9000
1547-7363
DOI:10.1090/tpms/1045