An improvement of the integrability of the state space of the $\Phi^4_3$-process and the support of the $\Phi ^4_3$-measure constructed by the limit of stationary processes of approximating stochastic quantization equations

Abstract

We improve the integrability of the state space of the $\Phi ^4_3$-process and the support of the $\Phi ^4_3$-measure on the torus obtained in [Albeverio, Kusuoka, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 2020]. For the improvement, we improve the estimates of the H\"older continuity in time of the solutions to approximation equations. In the present paper, we only discuss the estimates different from those in [Albeverio, Kusuoka, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 2020].