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

Jonas Teuwen

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)

Abstract

This paper presents a closed-form expression for the integral kernels associated with the derivatives of the Ornstein–Uhlenbeck semigroup e tL  etL. Our approach is to expand the Mehler kernel into Hermite polynomials and apply the powers L N  LN of the Ornstein–Uhlenbeck operator to it, where we exploit the fact that the Hermite polynomials are eigenfunctions for L L. As an application we give an alternative proof of the kernel estimates by Ref. 10, making all relevant quantities explicit.


Original languageEnglish
Article number1650030
Pages (from-to)1-13
Number of pages13
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume19
Issue number4
DOIs
Publication statusPublished - 2016

Keywords

  • Ornstein–Uhlenbeck
  • Mehler kernel
  • Gaussian measure
  • Hermite polynomials
  • Caldéron reproducing formula

Fingerprint

Dive into the research topics of 'On the integral kernels of derivatives of the Ornstein–Uhlenbeck semigroup'. Together they form a unique fingerprint.

Cite this