Lie symmetry methods for multi-dimensional parabolic PDEs and diffusions

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Journal Article
Journal of Differential Equations, 2012, 252 (1), pp. 56 - 90
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In this paper we introduce new methods based upon integrating Lie symmetries for the construction of explicit fundamental solutions of multi-dimensional second order parabolic PDEs. We present applications to the problem of finding transition probability densities for multi-dimensional diffusions and to representation theory. Many explicit examples are given to illustrate the techniques. © 2011 Elsevier Inc.
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