Heat Kernel Analysis for Ornstein-Uhlenbeck Operators with Quadratic Potentials

Sheng-Ya Feng

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arXiv · 1208.4264

Heat Kernel Analysis for Ornstein-Uhlenbeck Operators with Quadratic Potentials

Sheng-Ya Feng

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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.

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Sheng-Ya Feng. 2012-08-21. Heat Kernel Analysis for Ornstein-Uhlenbeck Operators with Quadratic Potentials. https://arxiv.org/abs/1208.4264

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