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.
CITATION STYLE
Marinelli, C., & Scarpa, L. (2021). On the Positivity of Local Mild Solutions to Stochastic Evolution Equations. In Springer Proceedings in Mathematics and Statistics (Vol. 378, pp. 231–245). Springer. https://doi.org/10.1007/978-3-030-87432-2_12
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