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UID:20250719T113303EDT-4011tVdHgu@132.216.98.100
DTSTAMP:20250719T153303Z
DESCRIPTION:Parabolic Anderson Model with space-time homogeneous Gaussian n
 oise and rough initial condition.\n\nThe goal of this talk is to illustrat
 e how various quantitative properties of the noise combined with the rough
 ness of the initial condition may affect the existence of a random field s
 olution of an SPDE\, and to describe the impact of the noise and the initi
 al condition on the behaviour of this solution. More precisely\, we will c
 onsider the Parabolic Anderson Model on $mathbb{R}_{+} imes mathbb{R}^d$ d
 riven by a space-time homogeneous Gaussian noise\, with initial condition 
 given by a signed measure. We assume that the covariance kernels of the no
 ise in space and time are given by locally integrable non-negative-definit
 e functions. We show that the solution to this equation exists and has a H
 ölder continuous modification\, under the same respective conditions as in
  the case of the white noise in time. This shows that the temporal structu
 re of the noise has no effect on the existence and Hölder regularity of th
 e solution. However\, the smoothness of the noise in time plays a big role
  in the order of magnitude of the moments of the solution.\n	\n	This talk is
  based on joint work with Le Chen (University of Kansas).\n
DTSTART:20161117T213000Z
DTEND:20161117T223000Z
LOCATION:Room 1205\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Raluca Balan\, Ottawa
URL:/mathstat/channels/event/raluca-balan-ottawa-26410
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