An improvement of the integrability of the state space of the Φ43-process and the support of the Φ43-measure constructed by the limit of stationary processes of approximating stochastic quantization equations

This is a remark paper for the Φ⁴₃ -measure and the associated flow on the torus which are constructed in [1] by the limit of the stationary processes of the stochastic quantization equations of approximation measures. We improve the integrability of the state space of the Φ⁴₃ -process and the support of the Φ⁴₃ -measure. For the improvement, we improve the estimates of the Hölder continuity in time of the solutions to approximation equations. In the present paper, we only discuss the estimates different from those in [1].

Mathematics Subject Classification. Primary 60H17; Secondary 81S20, 81T08, 60H15, 35Q40, 35R60, 35K58.