Hypothesis Testing for Fractional Stochastic Partial Differential Equations with Applications to Neurophysiology and Finance

Abstract

The paper obtains explicit form of fine large deviation theorems for the log-likelihood ratio in testing fractional stochastic partial differential equation models using a finite number of Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and colored (fractional) in time with Hurst parameter H ≥ 1/2. It obtains explicit rates of decrease of the error probabilities of Neyman-Pearson, Bayes and minimax tests. Finally, it provides several examples including two practical examples of membrane voltage model from neurophysiology and forward interest rate model from finance.