Markov properties for Gaussian fields associated with Dirichlet forms

TL;DR

This paper establishes the equivalence between local properties of Dirichlet forms and the Markov property of associated Gaussian fields, and introduces a strong Markov property with conditions for its validity.

Contribution

It proves the equivalence of local Dirichlet form properties and Gaussian field Markov properties, and defines a strong Markov property with sufficient conditions.

Findings

Proved equivalence between local Dirichlet form property and Gaussian field Markov property.

Introduced a strong Markov property for Gaussian fields.

Provided sufficient conditions for the strong Markov property to hold.

Abstract

We prove the equivalence of the local property for an irreducible regular Dirichlet form and the Markov property for the Gaussian field associated with the Dirichlet form. Moreover we introduce a strong Markov property for Gaussian fields and present some sufficient conditions for this to hold.