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

Author

Listed:
  • Igor Cialenco

    (Illinois Institute of Technology)

  • Hyun-Jung Kim

    (Illinois Institute of Technology)

  • Sergey V. Lototsky

    (University of Southern California)

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.

Suggested Citation

  • Igor Cialenco & Hyun-Jung Kim & Sergey V. Lototsky, 2020. "Statistical analysis of some evolution equations driven by space-only noise," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 83-103, April.
    • Handle: RePEc:spr:sistpr:v:23:y:2020:i:1:d:10.1007_s11203-019-09205-0
    DOI: 10.1007/s11203-019-09205-0
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    References listed on IDEAS

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    1. Igor Cialenco, 2018. "Statistical inference for SPDEs: an overview," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 309-329, July.
    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. Cialenco, Igor & Kim, Hyun-Jung, 2022. "Parameter estimation for discretely sampled stochastic heat equation driven by space-only noise," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 1-30.

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