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UID:20250702T071708EDT-7915C73xrF@132.216.98.100
DTSTAMP:20250702T111708Z
DESCRIPTION:Title: Recent advances on SPDEs using the random field approach
 .\n\nAbstract: In a seminal article in 1944\, It^o introduced the stochast
 ic integral with respect to the Brownian motion\, which turned out to be o
 ne of the most fruitful ideas in mathematics in the 20th century. This lea
 d to the development of stochastic analysis\, a field which includes the s
 tudy of stochastic partial differential equations (SPDEs). One of the appr
 oaches for the study of SPDEs was initiated by Walsh (1986) and relies on 
 the concept of random-field solution. This concept allows us to investigat
 e the probabilistic behavior of the solution to an SPDE\, simultaneously i
 n time and space. In this talk\, we will consider the stochastic heat equa
 tion and the stochastic wave equation on the entire space\, perturbed by 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 time li
 ke a process with stationary increments\, for instance the fractional Brow
 nian motion (fBm). Since fBm is not a semi-martingale\, It^o calculus tech
 niques cannot be applied in this case. The methods that we will present ar
 e based on Malliavin calculus. Without going into technical details\, this
  talk will illustrate the dynamical interplay between the regularity of th
 e noise and various properties of the solution (such as intermittency and 
 Feyman-Kac representations).\n
DTSTART:20190412T180000Z
DTEND:20190412T190000Z
LOCATION:Room VCH-2810\, CA\, Université Laval
SUMMARY:Raluca Balan\, University of Ottawa
URL:/mathstat/channels/event/raluca-balan-university-o
 ttawa-295946
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