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

Yingchao Xie and Xicheng Zhang

Stochastic Processes and their Applications, 2017, vol. 127, issue 10, 3228-3250

Abstract: In this paper we extend an inequality of Lenglart et al. (1980, Lemma 1.1) to general continuous adapted stochastic processes with values in topological spaces. Using this inequality we prove Burkholder–Davies–Gundy’s inequality for stochastic integrals in Orlicz-type spaces (a class of quasi-Banach spaces) with respect to cylindrical Brownian motions. As an application, we show the well-posedness of stochastic heat equations in Orlicz spaces.

Keywords: Stochastic integral; Good λ-inequality; BDG’s inequality; Orlicz space; Quasi-Banach space; Regularly varying function (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:10:p:3228-3250

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DOI: 10.1016/j.spa.2017.02.006

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