Stochastic integrals and BDG's inequalities in Orlicz-type spaces

Abstract

In this paper we extend an inequality of Lenglart, Lépingle and Pratelli \cite[Lemma 1.1]{LLP} to general continuous adapted stochastic processes with values in topology spaces. By this inequality we show Burkholder-Davies-Gundy's inequality for stochastic integrals in Orlicz-type spaces (a class of quasi-Banach spaces) with respect to cylindrical Brownian motions.

17pages