Positivity of mild solution to stochastic evolution equations with an application to forward rates
Abstract
We prove a maximum principle for mild solutions to stochastic evolution equations with (locally) Lipschitz coefficients and Wiener noise on weighted L2 spaces. As an application, we provide sufficient conditions for the positivity of forward rates in the Heath-Jarrow-Morton model, considering the associated Musiela SPDE on a homogeneous weighted Sobolev space.
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