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

作者：Roeckner, Michael; Zhu, Rongchan; Zhu, Xiangchan^*

来源：Forum Mathematicum, 2015, 27(3): 1657-1687.

DOI：10.1515/forum-2012-0137

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

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 Gamma in a Banach space E. We prove the existence of a martingale solution of this problem if Gamma is a regular convex set.

• 出版日期2015-5
• 单位北京理工大学; 北京交通大学