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 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.
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 -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.
Mots clés : Functional SPDE, Dini continuity, time delay, log-Harnack inequality, gradient estimate
Xing Huang 1 ; Feng-Yu Wang 2
CC-BY 4.0
@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},
pages = {519--537},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 26},
number = {2},
year = {2017},
doi = {10.5802/afst.1544},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1544/}
}
TY - JOUR AU - Xing Huang AU - Feng-Yu Wang TI - Functional SPDE with Multiplicative Noise and Dini Drift JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2017 SP - 519 EP - 537 VL - 26 IS - 2 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1544/ DO - 10.5802/afst.1544 LA - en ID - AFST_2017_6_26_2_519_0 ER -
%0 Journal Article %A Xing Huang %A Feng-Yu Wang %T Functional SPDE with Multiplicative Noise and Dini Drift %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2017 %P 519-537 %V 26 %N 2 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1544/ %R 10.5802/afst.1544 %G en %F AFST_2017_6_26_2_519_0
Xing Huang; Feng-Yu Wang. Functional SPDE with Multiplicative Noise and Dini Drift. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 26 (2017) no. 2, pp. 519-537. doi : 10.5802/afst.1544. https://afst.centre-mersenne.org/articles/10.5802/afst.1544/
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