Hypothesis Testing for Fractional Stochastic Partial Differential Equations with Applications to Neurophysiology and Finance
Jaya P. N. Bishwal *
Department of Mathematics and Statistics, University of North Carolina at Charlotte, 376 Fretwell Bldg., 9201 University City Blvd., Charlotte, NC 28223, USA.
*Author to whom correspondence should be addressed.
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.
Keywords: Stochastic partial differential equations, fractional Brownian motion, colored noise, hypothesis testing, Neyman-Pearson test, Bayes test, minimax test, large deviations