Drift Estimation for Stochastic Partial Differential Equation Driven by Fractional Brownian Motion

This paper presents a systematic asymptotic analysis of the least squares estimator (LSE) for the drift parameter in a fractional stochastic heat equation driven by fractional Brownian motion. Fractional Brownian motion, capable of capturing stylized features in financial markets such as long memory, has become an important modeling tool in financial econometrics and risk management. Based on continuous-time observations of the Fourier coefficients of the solution, we first establish the strong consistency and asymptotic normality of the estimator. We then construct an alternative estimator based on the LSE and analyze its asymptotic behavior. This study provides new asymptotic inference tools for stochastic systems with long-memory properties and extends the theoretical framework for parameter estimation in fractional stochastic partial differential equations.