Linear Stochastic Differential-Algebraic Equations

A Differential-Algeraic Equation is, essentially,
an Ordinary Differential Equation F(x,dot x)=0 that cannot be
solved for the derivative dot x . In a recent joint paper with
A. Alabert of UAB, Barcelona, we studied the linear stochastic
differential-algebraic equations with constant coefficients and
additive white noise. Due to the nature of this class of equations,
the solution must be defined as a generalized process. In the talk
I will present the results of this paper, providing a sufficient
condition for the existence of the density of the law of the solution.