Existence and approximation of Hunt processes associated with generalized Dirichlet forms

TL;DR

This paper proves the existence of Hunt processes linked to generalized Dirichlet forms under mild conditions and demonstrates their approximation by multivariate Poisson processes, extending previous results in the field.

Contribution

It establishes the association of Hunt processes with generalized Dirichlet forms satisfying D3 and provides a new approximation method using multivariate Poisson processes.

Findings

Hunt processes exist for strictly quasi-regular generalized Dirichlet forms satisfying D3.

The associated Hunt process can be approximated by multivariate Poisson processes.

The results extend and unify previous existence proofs for such processes.

Abstract

We show that any strictly quasi-regular generalized Dirichlet form that satisfies the mild structural condition D3 is associated to a Hunt process, and that the associated Hunt process can be approximated by a sequence of multivariate Poisson processes. This also gives a new proof for the existence of a Hunt process associated to a strictly quasi-regular generalized Dirichlet form that satisfies SD3 and extends all previous results.