Spectral Method for Analysis of Switching Diffusions

The analysis problem of switching diffusions is considered. This paper presents a new approach based on the spectral method formalism for solving generalized Fokker-Planck equations. The proposed method allows to transform partial differential equations into the linear algebraic equations, and to arrive at a solution in an explicit form. The aspects of applications are discussed. A numerical example is given to illustrate the efficiency of the proposed method.