Abstract for the talk on 25.02.2019 (14:00 h)
Arbeitsgemeinschaft ANGEWANDTE ANALYSISIvan Yaroslavtsev (TU Delft)
Burkholder-Davis-Gundy inequalities and stochastic integration in Banach spaces
In 1970s Burkholder, Davis, and Gundy proved the following inequalities which connect the Lp-norm of a martingale with its quadratic variation: <center class="math-display"> <img src="/fileadmin/lecture_img/tex_28574c0x.png" alt="????sup |Mt |p ≂p ???? [M ]p∞∕2,1 ≤ p &#x003C; ∞, t≥0 " class="math-display"></center>
where M is a real-valued martingale and [M] is the quadratic variation of M. These inequalities are known to be exceptionally important for stochastic integration theory as they yield sharp estimates for real-valued stochastic integrals. In this talk we present Burkholder-Davis-Gundy inequalities for martingales with values in general Banach spaces. As a corollary, we extend the theory of stochastic integration with respect to a general martingale to infinite dimensions.