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 |
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Pages (from-to) | 1657-1687 |
Number of pages | 31 |
Journal | Forum Mathematicum |
Volume | 27 |
Issue number | 3 |
DOIs | |
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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Röckner, M., Zhu, R., & Zhu, X. (2015). BV functions in a Gelfand triple for differentiable measure and its applications. Forum Mathematicum, 27(3), 1657-1687. https://doi.org/10.1515/forum-2012-0137