Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615422 | Journal of Mathematical Analysis and Applications | 2015 | 21 Pages |
Abstract
In this paper we introduce a variant of Burkholder's martingale transform associated with two martingales with respect to different filtrations. Even though the classical martingale techniques cannot be applied, we show that the discussed transformation still satisfies some expected Lp estimates. Then we apply the obtained inequalities to general-dilation twisted paraproducts, particular instances of which have already appeared in the literature. As another application we construct stochastic integrals â«0tHsd(XsYs) associated with certain continuous-time martingales (Xt)tâ¥0 and (Yt)tâ¥0. The process (XtYt)tâ¥0 is shown to be a “good integrator”, although it is not necessarily a semimartingale, or even adapted to any convenient filtration.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Vjekoslav KovaÄ, Kristina Ana Å kreb,