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.