Hypothesis testing for stochastic PDEs driven by additive noise

Igor Cialenco and Liaosha Xu

Stochastic Processes and their Applications, 2015, vol. 125, issue 3, 819-866

Abstract: We study the simple hypothesis testing problem for the drift coefficient for stochastic fractional heat equation driven by additive noise. We introduce the notion of asymptotically the most powerful test, and find explicit forms of such tests in two asymptotic regimes: large time asymptotics, and increasing number of Fourier modes. The proposed statistics are derived based on Maximum Likelihood Ratio. Additionally, we obtain a series of important technical results of independent interest: we find the cumulant generating function of the log-likelihood ratio; obtain sharp large deviation type results for T→∞ and N→∞.

Keywords: Hypothesis testing for SPDE; Maximum likelihood estimator; Asymptotically the most powerful test; Cumulant generating function; Fractional heat equation; Additive space–time white noise (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2014.09.022

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