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.
