"Fundamental Solutions for Parabolic Equations by Lie Symmetry Group Methods"

F. Güngör

(Istanbul Technical University, Department of Mathematics, Maslak, Istanbul)

Linear parabolic PDEs in 1+1-dimension, in particular Fokker-Planck
equations, arise in diverse areas such as diffusion processes,
stochastic (Markov) processes, Brownian motion, probability theory,
financial mathematics, population genetics, quantum chaos and others.
The efficiency of Lie symmetry methods for constructing fundamental
solutions (heat kernels) will be shown by way of examples like
harmonic oscillator (Mehler formula), the Ornstein-Uhlenbeck and
Bessel processes and Kolmogorov equation, among others. A new
criteria for transformability to canonical forms with four- and six-
dimensional finite symmetry groups will be presented.

Facultad de Ciencias

Seminario de Física Teórica
Universidad de Zaragoza