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We provide sufficient conditions on the coefficients of a stochasticevolution equation on a Hilbert space of functions driven by a cylindricalWiener process ensuring that its mild solution is positive if the initial datumis positive. As an application, we discuss the positivity of forward rates inthe Heath-Jarrow-Morton model via Musiela's stochastic PDE.

On the positivity of local mild solutions to stochastic evolution equations