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Functional SPDE with Multiplicative Noise and Dini Drift
Xing Huang; Feng-Yu Wang
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 26 (2017) no. 2, p. 519-537

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 L 2 -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.

Dans cet article, nous établissons l’existence, l’unicité et la non-explosion de la solution douce pour une classe d’équations aux dérivées partielles stochastiques semi-linéaires dont le bruit est multiplicatif et le drift satisfait la condition de Dini. Dans le cas de dimension finie et du temps de retard borné, nous montrons l’inégalité de Harnack logarithmique et une estimée de gradient dans L 2 pour la solution douce. Comme le semi-groupe Markovien est associé à la solution fonctionnelle de l’équation, nous devons étudier l’analyse sur l’espace des chemins des solutions définies sur l’intervalle du temps de retard.

Published online : 2017-04-13
DOI : https://doi.org/10.5802/afst.1544
Classification:  60H15,  60B10
Keywords: Functional SPDE, Dini continuity, time delay, log-Harnack inequality, gradient estimate
@article{AFST_2017_6_26_2_519_0,
     author = {Xing Huang and Feng-Yu Wang},
     title = {Functional SPDE with Multiplicative Noise and Dini Drift},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 26},
     number = {2},
     year = {2017},
     pages = {519-537},
     doi = {10.5802/afst.1544},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2017_6_26_2_519_0}
}
Huang, Xing; Wang, Feng-Yu. Functional SPDE with Multiplicative Noise and Dini Drift. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 26 (2017) no. 2, pp. 519-537. doi : 10.5802/afst.1544. afst.centre-mersenne.org/item/AFST_2017_6_26_2_519_0/

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