Existence, Regularity, and a Strong Itô Formula for the Isochronal Phase of SPDE

2021/09/09 by Zachary P. Adams, Adams, Zachary P.
Economics, Econometrics and Finance · Environmental Science · Mathematics · #Ecosystem dynamics and resilience #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2109.04515

openalex publication_date 2021/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence and regularity of the isochron map for stable invariant manifolds of a large class of evolution equations. Our results apply in particular to the isochron map of reaction-diffusion equations and neural field equations. Using the regularity properties proven here, we are able to obtain a strong Itô formula for the isochronal phase of stochastically perturbed travelling waves, spiral waves, and other patterns appearing in SPDEs driven by white noise, even for SPDEs that only admit mild solutions.

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