Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 19181, 24 pages

Fundamental solutions to Kolmogorov equations via reduction to canonical form

Joanna Goard

School of Mathematics and Applied Statistics, University of Wollongong, Wollongong 2522, NSW, Australia

Received 25 January 2006; Revised 11 May 2006; Accepted 13 June 2006

Copyright © 2006 Joanna Goard. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper finds fundamental solutions to the backward Kolmogorov equations, usually interpretable as transition density functions for variables x that follow certain stochastic processes of the form dx=A(x,t)dt+cxydX and dx=A(x,t)dt+α1+α2x+α3x2dX. This is achieved by first reducing the relevant PDEs that the density functions satisfy to their canonical form. These stochastic processes have direct realistic applications in the modeling of financial assets.