Spectral Analysis of Fokker--Planck and Related Operators Arising From Linear Stochastic Differential Equations

We study spectral properties of certain families of linear second-order differential operators arising from linear stochastic differential equations. We construct a basis in the Hilbert space of square-integrable functions using modified Hermite polynomials, and obtain a representation for these operators from which their eigenvalues and eigenfunctions can be computed. In particular, we completely describe the spectrum of the Fokker

• Type: Journal
• Year: 2000
• Where: SIAMCO
• Authors: Daniel Liberzon, Roger W. Brockett
• Keywords: Fokker­Planck Operator, Hermite Polynomials, Operator, SIAMCO 2000