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UID:20260828T223157EDT-1308m5wScP@132.216.98.100
DTSTAMP:20260829T023157Z
DESCRIPTION: \n\nStochastic heat equation: intermittency\, densities and be
 yond\n\nUPDATE: BURNSIDE HALL ROOM 306 - 15:00\n\nAbstract: Stochastic hea
 t equation (SHE) with multiplicative noise is an important model. When the
  diffusion coefficient is linear\, this model is also called the parabolic
  Anderson model\, the solution of which traditionally gives the Hopf-Cole 
 solution to the famous KPZ equation. Obtaining various fine properties of 
 its solution will certainly deepen our understanding of these important mo
 dels. In this talk\, I will highlight several interesting properties of SH
 E and then focus on the probability densities of the solution. In a recent
  joint work with Y. Hu and D. Nualart\, we establish a necessary and suffi
 cient condition for the existence and regularity of the density of the sol
 ution to SHE with measure-valued initial conditions. Under a mild cone con
 dition for the diffusion coefficient\, we establish the smooth joint densi
 ty at multiple points. The tool we use is Malliavin calculus. The main ing
 redient is to prove that the solutions to a related stochastic partial dif
 ferential equation have negative moments of all orders.\n
DTSTART:20161129T200000Z
DTEND:20161129T200000Z
LOCATION:Room 306\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Le Chen\, University of Kansas
URL:https://www.mcgill.ca/mathstat/channels/event/le-chen-university-kansas
 -264372
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