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

Michael Röckner, Rongchan Zhu, Xiangchan Zhu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)1657-1687
Number of pages31
JournalForum Mathematicum
Volume27
Issue number3
DOIs
Publication statusPublished - 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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