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

9 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

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AU - Zhu, Xiangchan

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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

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JF - Forum Mathematicum

IS - 3

ER -

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

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Keywords

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