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UID:20260620T054903EDT-8696wnZVml@132.216.98.100
DTSTAMP:20260620T094903Z
DESCRIPTION:Recent advances on SPDEs using the random field approach - Part
  I\n \n Abstract: In a seminal article in 1944\, Ito introduced the stocha
 stic integral with respect to the Brownian motion\, which turned out to be
  one of the most fruitful ideas in mathematics in the 20th century. This l
 ead to the development of stochastic analysis\, a field which includes the
  study of stochastic partial differential equations (SPDEs). One of the ap
 proaches for the study of SPDEs was initiated by Walsh (1986) and relies o
 n the concept of random-field solution. This concept allows us to investig
 ate the probabilistic behavior of the solution to an SPDE\, simultaneously
  in time and space.In these lectures\, we will consider the stochastic hea
 t equation and the stochastic wave equation on the entire space\, perturbe
 d by a Gaussian noise which is homogeneous in space (as introduced by Dala
 ng in 1999) and is 'colored' in time. This means that the noise behaves in
  time like a process with stationary increments\, for instance the fractio
 nal Brownian motion (fBm). Since fBm is not a semi-martingale\, Ito calcul
 us techniques cannot be applied in this case. The methods that we will pre
 sent are based on Malliavin calculus. Without going into technical details
 \, the lectures will illustrate the dynamical interplay between the regula
 rity of the noise and various properties of the solution (such as intermit
 tency and Feyman-Kac representations).
DTSTART:20181129T200000Z
DTEND:20181129T220000Z
LOCATION:CA\, QC\, Montreal\, H3T 1N8\, CRM\, Universite de Montreal\, 2920
 \, chemin de la Tour\,
SUMMARY:Raluca Balan\, University of Ottawa
URL:/mathstat/channels/event/raluca-balan-university-o
 ttawa-292020
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