2000 character limit reached
On the positivity of local mild solutions to stochastic evolution equations (1912.13259v1)
Published 31 Dec 2019 in math.AP, math.PR, and q-fin.MF
Abstract: We provide sufficient conditions on the coefficients of a stochastic evolution equation on a Hilbert space of functions driven by a cylindrical Wiener process ensuring that its mild solution is positive if the initial datum is positive. As an application, we discuss the positivity of forward rates in the Heath-Jarrow-Morton model via Musiela's stochastic PDE.