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Lie symmetry methods for multi-dimensional parabolic PDEs and diffusions. (English) Zbl 1242.35008

Summary: 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.

MSC:

35A08 Fundamental solutions to PDEs
35B06 Symmetries, invariants, etc. in context of PDEs
35K10 Second-order parabolic equations

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