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Functional SPDE with Multiplicative Noise and Dini Drift

Xing Huang, Feng-yu Wang Orcid Logo

Annales de la faculté des sciences de Toulouse Mathématiques, Volume: 26, Issue: 2, Pages: 519 - 537

Swansea University Author: Feng-yu Wang Orcid Logo

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DOI (Published version): 10.5802/afst.1544

Abstract

Existence, uniqueness and non-explosion of the mild solution are proved for a class of semi-linear functional SPDEs with multiplicative noise and Dini continuous drifts. In the finite-dimensional and bounded time delay setting, the log-Harnack inequality and L2-gradient estimate are derived. As the M...

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Published in: Annales de la faculté des sciences de Toulouse Mathématiques
ISSN: 0240-2963 2258-7519
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa33134
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Abstract: Existence, uniqueness and non-explosion of the mild solution are proved for a class of semi-linear functional SPDEs with multiplicative noise and Dini continuous drifts. In the finite-dimensional and bounded time delay setting, the log-Harnack inequality and L2-gradient estimate are derived. As the Markov semigroup is associated to the functional solution of the equation, one needs to make analysis on the path space of the solution in the time interval of delay。
College: Faculty of Science and Engineering
Issue: 2
Start Page: 519
End Page: 537