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

TL;DR

This paper enhances the understanding of the $\

Contribution

It introduces improved estimates for the solutions of approximation equations, leading to better integrability and support properties of the $\

Findings

Enhanced integrability of the $\

Improved estimates of Hölder continuity in time

Refined support of the $\

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].