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Estimation of an Unknown Parameter in the Cauchy Problem for a First-Order Partial Differential Equation under Small Gaussian Perturbations

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Abstract

On the basis of observation of a realization of a solution of the Cauchy problem, we establish a maximum-likelihood estimate for an unknown parameter. We construct an exponential inequality for the probabilities of large deviations of the estimate from the real value of the parameter.

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Authors and Affiliations

  1. Donbass Academy of Architecture, Donetsk

    A. A. Simogin

  2. Donetsk University, Donetsk

    B. V. Bondarev & A. I. Dzundza

Authors
  1. A. A. Simogin
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  2. B. V. Bondarev
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  3. A. I. Dzundza
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Simogin, A.A., Bondarev, B.V. & Dzundza, A.I. Estimation of an Unknown Parameter in the Cauchy Problem for a First-Order Partial Differential Equation under Small Gaussian Perturbations. Ukrainian Mathematical Journal 52, 1147–1155 (2000). https://doi.org/10.1023/A:1005298221276

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  • DOI: https://doi.org/10.1023/A:1005298221276

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