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Symmetry Group Methods for Fundamental Solutions and Characteristic Functions
"... This paper uses Lie symmetry group methods to analyse a class of partial differential equations of the form 2 + f(x) @u @x It is shown that when the drift function f is a solution of a family of Ricatti equations, then symmetry techniques can be used to find the characteristic functions a ..."
Abstract

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This paper uses Lie symmetry group methods to analyse a class of partial differential equations of the form 2 + f(x) @u @x It is shown that when the drift function f is a solution of a family of Ricatti equations, then symmetry techniques can be used to find the characteristic functions and transition densities of the corresponding diffusion processes.