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Geometric Analysis on Ornstein–Uhlenbeck Operators with Quadratic Potentials

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Abstract

In this paper, we study Ornstein–Uhlenbeck operators with quadratic potentials. We use Hamiltonian formalism to characterize the singularities produced by the potentials by finding explicit geodesics which are induced by the operators. Then we obtain the heat kernels via a probabilistic ansatz. All the formulae are closed.

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Authors and Affiliations

  1. Department of Mathematics and Department of Computer Science, Georgetown University, Washington, DC, 20057, USA

    Der-Chen Chang

  2. Department of Mathematics, Fu Jen Catholic University, Taipei, 242, Taiwan, ROC

    Der-Chen Chang

  3. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, P.R. China

    Sheng-Ya Feng

Authors
  1. Der-Chen Chang
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  2. Sheng-Ya Feng
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Corresponding author

Correspondence to Sheng-Ya Feng.

Additional information

Communicated by Steven G. Krantz.

D.-C. Chang is partially supported by an NSF grant DMS-1203845 and Hong Kong RGC competitive earmarked research grant #601410.

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Chang, DC., Feng, SY. Geometric Analysis on Ornstein–Uhlenbeck Operators with Quadratic Potentials. J Geom Anal 24, 1211–1232 (2014). https://doi.org/10.1007/s12220-012-9370-9

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  • DOI: https://doi.org/10.1007/s12220-012-9370-9

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