Uncertainty Quantification Seminar Ivan Yaroslavtsev (TU Delft)

Ivan Yaroslavtsev is working on stochastic analysis in Banach spaces, harmonic analysis, and Gaussian measures on infinite-dimensional spaces.
  • What Scientific Computing English Seminars
  • When 21-02-2019 from 15:00 to 16:00 (Europe/Amsterdam / UTC100)
  • Where Korteweg-de Vries Institute, room F1.15
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Title: Burkholder-Davis-Gundy inequalities and stochastic integration in UMD Banach spaces

Abstract: In this talk we will present Burkholder--Davis--Gundy inequalities for general UMD Banach space-valued martingales. Namely, we will show that for any UMD Banach space X, for any X-valued martingale M with M_0=0, and for any 1 \leq p < infty:
E sup_{0 \leq s \leq t} ||M_s||^p \eqsim_{p, X} E gamma([M]_t)^p,   t \geq 0,

where [M]_t is the covariation bilinear form of M defined on X* x X* by

[M]_t(x*, y*) = [<M,x*>,<M, y*>]_t,   for x*, y* in X*,

and gamma([M]_t) is the L2-norm of a Gaussian measure on X having [M]_t as its covariance bilinear form.

As a consequence we will extend the theory of vector-valued stochastic integration with respect to a cylindrical Brownian motion by van Neerven, Veraar, and Weis, to the full generality.