Small-Time Asymptotic Behavior of the Stochastic Landau--Lifshitz--Baryakhtar Equation

Abstract

We establish a small-time large deviation principle for the stochastic Landau--Lifshitz--Baryakhtar equation using the framework of exponential equivalence. This result characterizes the asymptotic behavior of the solution on very short time scales. In particular, it shows that, as the stochastic thermal fluctuations become small, the magnetization remains exponentially concentrated near its initial state, reflecting the short-time stability of the magnetization dynamics. The associated rate function provides a quantitative measure of deviations from the initial state and the resulting short-time stability.