One modification of the martingale transform and its applications to paraproducts and stochastic integrals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:426

Article

Kovac, Vjekoslav¹  Skreb, Kristina Ana² 

[1] Univ Zagreb, Fac Sci, Dept Math, Zagreb 10000, Croatia

[2] Univ Zagreb, Fac Civil Engn, Zagreb 10000, Croatia

关键词: Martingale transform;    Paraproduct;    Bellman function;    Space of homogeneous type;    Stochastic integral;    Ito construction;   

DOI  :  10.1016/j.jmaa.2015.02.015

来源: Elsevier

【 摘 要 】

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 L-p 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 integral(t)(0) H(s)d(XsYs) associated with certain continuous-time martingales (X-t)(t >= 0) and (Y-t)(t >= 0). The process (XtYt)(t >= 0) is shown to be a good integrator, although it is not necessarily a semimartingale, or even adapted to any convenient filtration. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free