Statistical analysis of some evolution equations driven by space-only noise

Igor Cialenco (), Hyun-Jung Kim () and Sergey V. Lototsky ()
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Igor Cialenco: Illinois Institute of Technology
Hyun-Jung Kim: Illinois Institute of Technology
Sergey V. Lototsky: University of Southern California

Statistical Inference for Stochastic Processes, 2020, vol. 23, issue 1, No 3, 83-103

Abstract: Abstract We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the solution, for such equations have been studied, little is known about inverse problems for these equations. We exploit the somewhat unusual structure of the observations coming from these equations that leads to an interesting interplay between classical and non-traditional statistical models. We derive several types of estimators for the drift and/or diffusion coefficients of these equations, and prove their relevant properties.

Keywords: Stochastic PDEs; MLE; Bayesian estimators; Local asymptotic normality; Regular statistical model; Parabolic Anderson model; shell model; Multi-channel model; Primary 62F12; Secondary 60H15; 93E10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11203-019-09205-0

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