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^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	3228-3250
Number of pages	23
Journal	Stochastic Processes and their Applications
Volume	127
Issue number	10
DOIs	https://doi.org/10.1016/j.spa.2017.02.006
Publication status	Published - Oct 2017
Externally published	Yes

Keywords

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

Access to Document

10.1016/j.spa.2017.02.006

Cite this

@article{8a99574a247b48c2830bea7012c5cbf6,

title = "Stochastic integrals and BDG's inequalities in Orlicz-type spaces",

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",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2017",

month = oct,

doi = "10.1016/j.spa.2017.02.006",

language = "English",

volume = "127",

pages = "3228--3250",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier B.V.",

number = "10",

}

TY - JOUR

T1 - Stochastic integrals and BDG's inequalities in Orlicz-type spaces

AU - Xie, Yingchao

AU - Zhang, Xicheng

PY - 2017/10

Y1 - 2017/10

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

UR - http://www.scopus.com/inward/record.url?scp=85015702216&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2017.02.006

DO - 10.1016/j.spa.2017.02.006

M3 - Article

AN - SCOPUS:85015702216

SN - 0304-4149

VL - 127

SP - 3228

EP - 3250

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this