One modification of the martingale transform and its applications to paraproducts and stochastic integrals (CROSBI ID 215989)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Kovač, Vjekoslav ; Škreb, Kristina Ana
engleski
One modification of the martingale transform and its applications to paraproducts and stochastic integrals
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 associated with certain continuous-time martingales. The product process is shown to be a "good integrator", although it is not necessarily a semimartingale, or even adapted to any convenient filtration.
martingale transform ; paraproduct ; multilinear estimate ; the Bellman function ; space of homogeneous type ; stochastic integral ; the Bichteler-Dellacherie theorem ; the Ito construction
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Podaci o izdanju
426 (2)
2015.
1143-1163
objavljeno
0022-247X
10.1016/j.jmaa.2015.02.015