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

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 [RZZ12], 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.

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