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Parameter Estimation for Stochastic Partial Differential Equations of Second Order

  • Josef Janák
Article
  • 60 Downloads

Abstract

Stochastic partial differential equations of second order with two unknown parameters are studied. Based on ergodicity, two suitable families of minimum contrast estimators are introduced. Strong consistency and asymptotic normality of estimators are proved. The results are applied to hyperbolic equations perturbed by Brownian noise.

Keywords

Parameter estimation Strong consistency Asymptotic normality 

Mathematics Subject Classification

62M05 93E10 60G35 60H15 

References

  1. 1.
    Bishwal, J.P.N.: Parameter estimation in stochastic differential equations. In: Lecture Notes in Mathematics. Springer, New York (2008)Google Scholar
  2. 2.
    Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions. Cambridge University Press, Cambridge (1992)CrossRefzbMATHGoogle Scholar
  3. 3.
    Iacus, S.M.: Simulation and Inference for Stochastic Differential Equations. Springer Series in Statistics. Springer, New York (2008)CrossRefzbMATHGoogle Scholar
  4. 4.
    Koski, T., Loges, W.: On identification for distributed parameter systems. Stochastic Processes—Mathematics and Physics II, Proceedings of the 2nd BiBoS Symposium, pp. 152–159 (1985)Google Scholar
  5. 5.
    Koski, T., Loges, W.: Asymptotic statistical inference for a stochastic heat flow problem. Stat. Probab. Lett. 3(4), 185–189 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kutoyants, Y.A.: Statistical Inference for Ergodic Diffusion Processes. Springer, London (2004)CrossRefzbMATHGoogle Scholar
  7. 7.
    Maslowski, B., Pospíšil, J.: Ergodicity and parameter estimates for infinite-dimensional fractional Ornstein–Uhlenbeck process. Appl. Math. Optim. 57(3), 401–429 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Maslowski, B., Tudor, C.A.: Drift parameter estimation for infinite-dimensional fractional Ornstein-Uhlenbeck process. Bull. Sci. Math. 137(7), 880–901 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Tudor, C.A., Viens, F.G.: Statistical aspects of the fractional stochastic calculus. Ann. Stat. 35(3), 1183–1212 (2007)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Economics in PraguePrague 4Czech Republic

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