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Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency
Hu, Yaozhong Huang, Jingyu Nualart, David Tindel, Samy
Hu, Yaozhong
Huang, Jingyu
Nualart, David
Tindel, Samy
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Abstract
This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W is a mean zero Gaussian noise and the differential element uW is interpreted both in the sense of Skorohod and Stratonovich. The existence and uniqueness of the solution are studied for noises with general time and spatial covariance structure. Feynman-Kac formulas for the solutions and for the moments of the solutions are obtained under general and different conditions. These formulas are applied to obtain the Hölder continuity of the solutions. They are also applied to obtain the intermittency bounds for the moments of the solutions.
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2016-06-04
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Institute of Mathematical Statistics
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Hu_2015_IMS.pdf
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Fractional Brownian motion, Malliavin calculus, Skorohod integral, Young's integral, Stochastic partial differential equations, Feynman-Kac formula, Intermittency
Citation
Hu, Yaozhong; Huang, Jingyu; Nualart, David; Tindel, Samy. Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency. Electron. J. Probab. 20 (2015), paper no. 55, 50 pp. doi:10.1214/EJP.v20-3316. http://projecteuclid.org/euclid.ejp/1465067161.