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We prove an existence and uniqueness theorem for stochastic reaction±diffusion equations driven by space-time white noise in one spatial dimension, when the diffusion coef®cient is non-degenerate and the force term is only measurable and can be locally unbounded.

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.

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