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Lie Symmetry Methods for Multidimensional Linear, Parabolic PDES and Diffusions

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  • Mark Craddock

    (Department of Mathematical Sciences, University of Technology Sydney)

  • Kelly A. Lennox

    (Department of Mathematical Sciences, University of Technology Sydney)

Abstract

In this paper we introduce methods based upon Lie symmetry analysis for the construction of explicit fundamental solutions of multidimensional parabolic PDEs. We give applications to the problem of finding transition probability densities for multidimensional diffusions and to representation theory.

Suggested Citation

  • Mark Craddock & Kelly A. Lennox, 2010. "Lie Symmetry Methods for Multidimensional Linear, Parabolic PDES and Diffusions," Research Paper Series 274, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:274
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp274.pdf
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    Keywords

    Lie symmetry groups; fundamental solutions; transition densities; representation theory;

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