Gibbs measures with double stochastic integrals on a path space

Volker Betz, Fumio Hiroshima

Published 2007-07-23, updated 2008-01-31Version 2

We investigate Gibbs measures relative to Brownian motion in the case when the interaction energy is given by a double stochastic integral. In the case when the double stochastic integral is originating from the Pauli-Fierz model in nonrelativistic quantum electrodynamics, we prove the existence of its infinite volume limit.