We consider 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 generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.
Aureli Alabert. Marco Ferrante. "Linear stochastic differential-algebraic equations with constant coefficients." Electron. Commun. Probab. 11 316 - 335, 2006. https://doi.org/10.1214/ECP.v11-1236