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arXiv · 1509.05702

On the integral kernels of derivatives of the Ornstein-Uhlenbeck semigroup

Jonas Teuwen
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Abstract

This paper presents a closed-form expression for the integral kernels associated with the derivatives of the Ornstein-Uhlenbeck semigroup $e^{tL}$. Our approach is to expand the Mehler kernel into Hermite polynomials and applying the powers $L^N$ of the Ornstein-Uhlenbeck operator to it, where we exploit the fact that the Hermite polynomials are eigenfunctions for $L$. As an application we give an alternative proof of the kernel estimates by Portal [2014], making all relevant quantities explicit.

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Jonas Teuwen. 2015-09-18. On the integral kernels of derivatives of the Ornstein-Uhlenbeck semigroup. https://doi.org/10.1142/s0219025716500302

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