Aureli Alabert, Marco Ferrante
Published 2005-07-07, updated 2006-07-03Version 2
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.
Comments: The paper has been rewritten in a more formal style, with rigorous proofs. In particular, Section 4 on absolute continuity of solutions has been completely rewritten
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