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Hypothesis testing for stochastic PDEs driven by additive noise

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  • Cialenco, Igor
  • Xu, Liaosha

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→∞.

Suggested Citation

  • Cialenco, Igor & Xu, Liaosha, 2015. "Hypothesis testing for stochastic PDEs driven by additive noise," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 819-866.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:3:p:819-866
    DOI: 10.1016/j.spa.2014.09.022
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    References listed on IDEAS

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    1. Pavel Gapeev & Uwe Küchler, 2008. "On large deviations in testing Ornstein–Uhlenbeck-type models," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 143-155, June.
    2. Igor Cialenco & Sergey Lototsky, 2009. "Parameter estimation in diagonalizable bilinear stochastic parabolic equations," Statistical Inference for Stochastic Processes, Springer, vol. 12(3), pages 203-219, October.
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    Cited by:

    1. Igor Cialenco & Ruoting Gong & Yicong Huang, 2018. "Trajectory fitting estimators for SPDEs driven by additive noise," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 1-19, April.
    2. Igor Cialenco, 2018. "Statistical inference for SPDEs: an overview," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 309-329, July.

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