Fundamental solutions, transition densities and the integration of Lie symmetries |
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Authors: | Mark Craddock |
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Affiliation: | Department of Mathematical Sciences, University of Technology Sydney, PO Box 123, Broadway, New South Wales 2007, Australia |
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Abstract: | In this paper we present some new applications of Lie symmetry analysis to problems in stochastic calculus. The major focus is on using Lie symmetries of parabolic PDEs to obtain fundamental solutions and transition densities. The method we use relies upon the fact that Lie symmetries can be integrated with respect to the group parameter. We obtain new results which show that for PDEs with nontrivial Lie symmetry algebras, the Lie symmetries naturally yield Fourier and Laplace transforms of fundamental solutions, and we derive explicit formulas for such transforms in terms of the coefficients of the PDE. |
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Keywords: | 35C05 35K15 60H99 60G99 |
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