| Abstract: |
| For general locally subcritical parabolic singular SPDEs without variance blow-up, we prove that the BPHZ model satisfies a Fernique-type theorem, namely exponential square integrability, whenever the driving noise is stationary and satisfies a suitable Poincare inequality. As applications, we obtain two consequences. First, if the SPDE admits appropriate a priori estimates, then its solution satisfies a corresponding concentration inequality. Second, we show that the BPHZ model satisfies a Schilder-type large deviation principle, and that the solution to the SPDE satisfies a Freidlin-Wentzell-type large deviation principle, extending the result of Hairer and Weber (2015). |
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