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UID:20260620T075446EDT-3624A8MdPH@132.216.98.100
DTSTAMP:20260620T115446Z
DESCRIPTION:Recent advances on SPDEs using the random field approach - Part
  II\nAbstract: In a seminal article in 1944\, Ito introduced the stochasti
 c integral with respect to the Brownian motion\, which turned out to be on
 e of the most fruitful ideas in mathematics in the 20th century. This lead
  to the development of stochastic analysis\, a field which includes the st
 udy of stochastic partial differential equations (SPDEs). One of the appro
 aches for the study of SPDEs was initiated by Walsh (1986) and relies on t
 he concept of random-field solution. This concept allows us to investigate
  the probabilistic behavior of the solution to an SPDE\, simultaneously in
  time and space.In these lectures\, we will consider the stochastic heat e
 quation and the stochastic wave equation on the entire space\, perturbed b
 y a Gaussian noise which is homogeneous in space (as introduced by Dalang 
 in 1999) and is 'colored' in time. This means that the noise behaves in ti
 me like a process with stationary increments\, for instance the fractional
  Brownian motion (fBm). Since fBm is not a semi-martingale\, Ito calculus 
 techniques cannot be applied in this case. The methods that we will presen
 t are based on Malliavin calculus. Without going into technical details\, 
 the lectures will illustrate the dynamical interplay between the regularit
 y of the noise and various properties of the solution (such as intermitten
 cy and Feyman-Kac representations).\n 
DTSTART:20181130T200000Z
DTEND:20181130T220000Z
LOCATION:CA\, QC\, Montreal\, H3T 1N8\, CRM\, Universite de Montreal\, 2920
  chemin de la Tour\, salle 5340
SUMMARY:Raluca Balan\, University of Ottawa
URL:/mathstat/channels/event/raluca-balan-university-o
 ttawa-292026
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