Title: Stability of ODEs with Colored Noise Forcing

Speaker: Timothy Blass, University of Texas at Austin

Date/Time: Tuesday, November 16, 2010, 9:00 am Mountain Time       

Location: CSRI Building/Room 279 (Sandia NM)

Brief Abstract: I will present a method for determining the stability of a class of stochastically forced ODEs, where the forcing term can be obtained by passing white noise through a filter of arbitrarily high degree. In the case of first order equations, by using the Fokker-Planck equation to write a PDE for the second moments, the question of stability can be recast as an eigenvalue problem for a second-order differential operator. Inspired by Dirac's creation and annihilation operator method, ``ladder'' operators are used to determine analytic expressions for the eigenvalues and eigenfunctions the differential operator. The first-order setting provides a framework for developing a perturbation theory for the case of higher-order equations. This work has been used to understand the stability of capillary waves in a time-changing gravitational field.

CSRI POC: Pavel Bochev, 844-1990