BV functions in a Gelfand triple for differentiable measure and its applications

Michael Röckner; Rongchan Zhu; Xiangchan Zhu

doi:10.1515/forum-2012-0137

BV functions in a Gelfand triple for differentiable measure and its applications

Michael Röckner, Rongchan Zhu, Xiangchan Zhu^*

^*Corresponding author for this work

School of Mathematics and Statistics

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

8 Citations (Scopus)

Abstract

In this paper, we introduce a definition of BV functions for (non-Gaussian) differentiable measure in a Gelfand triple which is an extension of the definition of BV functions in [Ann. Probab. 40 (2012), 1759-1794], using Dirichlet form theory. By this definition, we can analyze the reflected stochastic quantization problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set Γ in a Banach space E. We prove the existence of a martingale solution of this problem if Γ is a regular convex set.

Original language	English
Pages (from-to)	1657-1687
Number of pages	31
Journal	Forum Mathematicum
Volume	27
Issue number	3
DOIs	https://doi.org/10.1515/forum-2012-0137
Publication status	Published - 1 May 2015

Keywords

BV function
Dirichlet forms
Gelfand triples
differentiable measure
integration by parts formula in infinite dimensions
stochastic quantization
stochastic reflection problems

Access to Document

10.1515/forum-2012-0137

Cite this

@article{cecdb9e18c8343ae91ce910e21a84239,

title = "BV functions in a Gelfand triple for differentiable measure and its applications",

abstract = "In this paper, we introduce a definition of BV functions for (non-Gaussian) differentiable measure in a Gelfand triple which is an extension of the definition of BV functions in [Ann. Probab. 40 (2012), 1759-1794], using Dirichlet form theory. By this definition, we can analyze the reflected stochastic quantization problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set Γ in a Banach space E. We prove the existence of a martingale solution of this problem if Γ is a regular convex set.",

keywords = "BV function, Dirichlet forms, Gelfand triples, differentiable measure, integration by parts formula in infinite dimensions, stochastic quantization, stochastic reflection problems",

author = "Michael R{\"o}ckner and Rongchan Zhu and Xiangchan Zhu",

note = "Publisher Copyright: {\textcopyright} 2015 by De Gruyter.",

year = "2015",

month = may,

day = "1",

doi = "10.1515/forum-2012-0137",

language = "English",

volume = "27",

pages = "1657--1687",

journal = "Forum Mathematicum",

issn = "0933-7741",

publisher = "Walter de Gruyter GmbH",

number = "3",

}

TY - JOUR

T1 - BV functions in a Gelfand triple for differentiable measure and its applications

AU - Röckner, Michael

AU - Zhu, Rongchan

AU - Zhu, Xiangchan

PY - 2015/5/1

Y1 - 2015/5/1

N2 - In this paper, we introduce a definition of BV functions for (non-Gaussian) differentiable measure in a Gelfand triple which is an extension of the definition of BV functions in [Ann. Probab. 40 (2012), 1759-1794], using Dirichlet form theory. By this definition, we can analyze the reflected stochastic quantization problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set Γ in a Banach space E. We prove the existence of a martingale solution of this problem if Γ is a regular convex set.

AB - In this paper, we introduce a definition of BV functions for (non-Gaussian) differentiable measure in a Gelfand triple which is an extension of the definition of BV functions in [Ann. Probab. 40 (2012), 1759-1794], using Dirichlet form theory. By this definition, we can analyze the reflected stochastic quantization problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set Γ in a Banach space E. We prove the existence of a martingale solution of this problem if Γ is a regular convex set.

KW - BV function

KW - Dirichlet forms

KW - Gelfand triples

KW - differentiable measure

KW - integration by parts formula in infinite dimensions

KW - stochastic quantization

KW - stochastic reflection problems

UR - http://www.scopus.com/inward/record.url?scp=84929094497&partnerID=8YFLogxK

U2 - 10.1515/forum-2012-0137

DO - 10.1515/forum-2012-0137

M3 - Article

AN - SCOPUS:84929094497

SN - 0933-7741

VL - 27

SP - 1657

EP - 1687

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 3

ER -

BV functions in a Gelfand triple for differentiable measure and its applications

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this