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

Yingchao Xie; Xicheng Zhang

doi:10.1016/j.spa.2017.02.006

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

Yingchao Xie, Xicheng Zhang^*

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	3228-3250
页数	23
期刊	Stochastic Processes and their Applications
卷	127
期	10
DOI	https://doi.org/10.1016/j.spa.2017.02.006
出版状态	已出版 - 10月 2017
已对外发布	是

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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 = "BDG's inequality, Good λ-inequality, Orlicz space, Quasi-Banach space, Regularly varying function, Stochastic integral",

author = "Yingchao Xie and Xicheng Zhang",

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AU - Xie, Yingchao

AU - Zhang, Xicheng

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N2 - 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.

AB - 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.

KW - BDG's inequality

KW - Good λ-inequality

KW - Orlicz space

KW - Quasi-Banach space

KW - Regularly varying function

KW - Stochastic integral

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 10

ER -

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

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