An It^o Formula for Isochron Maps in Separable Hilbert Space

In this note, we prove an It^o formula for the isochron map of a reaction-diffusion system. This follows the proof of a new result which states that the second derivative of the isochron map of a reaction-diffusion system is trace class. This result, in turn, is a corollary of Proposition 2.3, which guarantees that the first and second Frechet derivatives of the flow of a reaction-diffusion system with respect to initial conditions are trace class.