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

2016/06/14 by Xie, Yingchao, Zhang, Xicheng
#60H05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1606.04350

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.

Related

• Nonlinear stochastic homogenization in Orlicz spaces and applications
• Cylindrical Wiener processes
• Orlicz-Sobolev inequalities for sub-Gaussian measures and ergodicity of Markov semi-groups
• Itô's Formula for Itô processes defined with respect to a cylindrical-martingale valued measure
• Sharp supremum and Hölder bounds for stochastic integrals indexed by a parameter