Some Norm Inequalities for Gaussian Wick Products

Abstract

We provide several inequalities for the ℒ ^q (𝒫)-norm of the Wick product of random variables. These estimates are based on a Jensen's type inequality for the Wick multiplication, which we derive via a positivity argument. As an application we study a certain type of anticipating stochastic differential equation whose solution is shown to be an element of ℒ ^q (𝒫) for some q ≥ 1.

Keywords:

• Jensen's inequality
• Second quantization operator
• Stochastic differential equations
• Wick product

AMS Subject Classification:

• 60H40
• 60H10