A new approach to Poincare-type inequalities on the Wiener space

作者：Lanconelli Alberto^*

来源：Stochastics and Dynamics, 2016, 16(1): 1650002.

DOI：10.1142/S0219493716500027

• Poincare inequality
• abstract Wiener space
• Wick product
• stochastic exponentials

We prove a new type of Poincare inequality on abstract Wiener spaces for a family of probability measures that are absolutely continuous with respect to the reference Gaussian measure. This class of probability measures is characterized by the strong positivity (a notion introduced by Nualart and Zakai in [22]) of their Radon-Nikodym densities. In general, measures of this type do not belong to the class of log-concave measures, which are a wide class of measures satisfying the Poincare inequality (Brascamp and Lieb [2]). Our approach is based on a pointwise identity relating Wick and ordinary products and on the notion of strong positivity which is connected to the non-negativity of Wick powers. Our technique also leads to a partial generalization of the Houdre and Kagan [11] and Houdre and Perez-Abreu [12] Poincare-type inequalities.

• 出版日期2016-2