## 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

DLMF
Full Text:

### References:

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