Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise
Balan, Raluca M. (University of Ottawa. Department of Mathematics and Statistics)
Quer i Sardanyons, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Song, Jian (Shandong University. School of Mathematics)

Data:	2019
Resum:	In this article, we consider the Parabolic Anderson Model with constant initial condition, driven by a space-time homogeneous Gaussian noise, with general covariance function in time and spatial spectral measure satisfying Dalang's condition. First, we prove that the solution (in the Skorohod sense) exists and is continuous in Lp (Ω). Then, we show that the solution has a modification whose sample paths are Hölder continuous in space and time, under the minimal condition on the spatial spectral measure of the noise (which is the same as the condition encountered in the case of the white noise in time). This improves similar results which were obtained in [6, 10] under more restrictive conditions, and with sub-optimal exponents for Hölder continuity.
Ajuts:	Ministerio de Economía y Competitividad MTM2015-67802P
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	60H07 ; 60H15 ; Gaussian noise ; Malliavin calculus ; Stochastic partial differential equations
Publicat a:	Acta Mathematica Scientia, Vol. 39, Issue 3 (May 2019) , p. 717-730, ISSN 1572-9087

DOI: 10.1007/s10473-019-0306-3

Postprint 16 p, 417.5 KB

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