@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",
}