Heat Kernel Analysis for Ornstein-Uhlenbeck Operators with Quadratic Potentials
Analysis of PDEs
2012-08-22 v1
Abstract
In this paper, we study Ornstein-Uhlenbeck operators with quadratic potentials. We use Hamiltonian formalism to characterise the singularities produced by the potentials by finding explicit geodesics of the operators, and obtain the heat kernels via a probabilistic ansatz. All the formulae are closed.
Cite
@article{arxiv.1208.4264,
title = {Heat Kernel Analysis for Ornstein-Uhlenbeck Operators with Quadratic Potentials},
author = {Sheng-Ya Feng},
journal= {arXiv preprint arXiv:1208.4264},
year = {2012}
}