Some non-linear s. p. d. e's that are second order in time.
Dalang, Robert C., Mueller, Carl (2003)
Electronic Journal of Probability [electronic only]
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Dalang, Robert C., Mueller, Carl (2003)
Electronic Journal of Probability [electronic only]
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Marco Ferrante, Marta Sanz-Solé (2006)
ESAIM: Probability and Statistics
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We study strictly parabolic stochastic partial differential equations on , ≥ 1, driven by a Gaussian noise white in time and coloured in space. Assuming that the coefficients of the differential operator are random, we give sufficient conditions on the correlation of the noise ensuring Hölder continuity for the trajectories of the solution of the equation. For self-adjoint operators with deterministic coefficients, the mild and weak formulation of the equation are...
Dalang, Robert C. (1999)
Electronic Journal of Probability [electronic only]
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Mireille Chaleyat-Maurel, Marta Sanz-Solé (2003)
ESAIM: Probability and Statistics
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We consider the random vector , where are distinct points of and denotes the stochastic process solution to a stochastic wave equation driven by a noise white in time and correlated in space. In a recent paper by Millet and Sanz–Solé [10], sufficient conditions are given ensuring existence and smoothness of density for . We study here the positivity of such density. Using techniques developped in [1] (see also [9]) based on Analysis on an abstract Wiener space, we characterize...
Márquez-Carreras, David, Sarrà, Mònica (2003)
Electronic Journal of Probability [electronic only]
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Bahlali, K., Elouaflin, A., N'zi, M. (2004)
Journal of Applied Mathematics and Stochastic Analysis
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Kolokol'tsov, V.N., Schilling, R.L., Tyukov, A.E. (2002)
Electronic Journal of Probability [electronic only]
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Denis, Laurent, Matoussi, Anis, Stoica, Lucretiu (2009)
Electronic Journal of Probability [electronic only]
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Wang, Jiajie, Ran, Qikang, Chen, Qihong (2007)
Journal of Applied Mathematics and Stochastic Analysis
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