Gradient Estimates and Maximal Dissipativity for the Kolmogorov Operator in $\Phi^4_2$.
Résumé
We consider the transition semigroup Pt of the $Φ 4 2$ stochastic quantisation on the torus $T 2$ and prove the following new estimate (Theorem 3.9) $|DPtϕ(x) · h| ≤ c t −β |h| C −s ϕ 0 (1 + |x| C −α) γ$ , for some $α, β, γ, s $positive. Thanks to this estimate, we show that cylindrical functions are a core for the corresponding Kolmogorov equation. Some consequences of this fact are discussed in a final remark.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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