Hypothesis Testing for Fractional Stochastic Partial Differential Equations with Applications to Neurophysiology and Finance
Asian Research Journal of Mathematics · pp. 1–24 · Published 2 May 2017
10.9734/ARJOM/2017/33094Abstract
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.
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