Symmetry and exact solutions of linear and nonlinear Kolmogorov equations

Abstract:
Symmetry properties of linear and nonlinear Kolmogorov equations arising in diffusion theory and in finance are investigated. The classification of subalgebras of Lie algebra of symmetry operators are carried out. Using these subalgebras the symmetry reduction of Kolmogorov equations to ordinary differential equations are fulfilled, and exact solutions of the researched equations are constructed. Also the separation of variables for linear Kolmogorov equations is carried out.