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SUMMARY:Stochastic calculus for non-semimartingales in Banach spaces and a
 n infinite dimensional PDE
DTSTART:20120323T101500
DTEND:20120323T111500
DTSTAMP:20260920T144901Z
UID:0ca30bca0a1f3087cc5c331cb3f76cd7ed0f8399b55b2b3caa708b40
CATEGORIES:Conferences - Seminars
DESCRIPTION:Cristina Di Girolami\nThis talk develops some aspects of stoch
 astic calculus via regularization for processes with values in a general B
 anach space B. A new concept of quadratic variation which depends on a par
 ticular subspace is introduced. An Itô formula and stability results for 
 processes admitting this kind of quadratic variation are presented. Partic
 ular interest is devoted to the case when B is thespace of real continuous
  functions defined on [−T\, 0]\, T > 0 and the process is the window pro
 cess X(·) associated with a continuous real process X which\, at time t\,
  it takes into account the past of the process. If X is a finite quadratic
  variation process\n(for instance Dirichlet\, weak Dirichlet)\, it is poss
 ible to represent a large class of pathdependent random variable h as a re
 al number plus a real forward integral in a semiexplicite form. This repre
 sentation result of h makes use of a functional solving an infinite dimens
 ional partial differential equation. This decomposition generalizes\, in s
 ome cases\, the Clark-Ocone formula which is true when X is the standard B
 rownian motion W.\nThis is a joint work with Francesco Russo (ENSTA ParisT
 ech).
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STATUS:CONFIRMED
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