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On the asymptotic behavior of solutions of the Cauchy problem for parabolic equations with time periodic coefficients

Author

Listed:
  • R. Z. Khasminskii

    (Wayne State University
    Institute of the Information Transmission Problems)

  • N. V. Krylov

    (University of Minnesota)

Abstract

We are considering the asymptotic behavior as $$t\rightarrow \infty $$ t → ∞ of solutions of the Cauchy problem for parabolic second order equations with time periodic coefficients. The problem is reduced to considering degenerate time-homogeneous diffusion processes on the product of a unit circle and Euclidean space.

Suggested Citation

  • R. Z. Khasminskii & N. V. Krylov, 2022. "On the asymptotic behavior of solutions of the Cauchy problem for parabolic equations with time periodic coefficients," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 3-16, April.
    • Handle: RePEc:spr:sistpr:v:25:y:2022:i:1:d:10.1007_s11203-021-09259-z
    DOI: 10.1007/s11203-021-09259-z
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    References listed on IDEAS

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    1. Reinhard Höpfner & Yury Kutoyants, 2010. "Estimating discontinuous periodic signals in a time inhomogeneous diffusion," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 193-230, October.
    2. Dominique Dehay, 2015. "Parameter maximum likelihood estimation problem for time periodic modulated drift Ornstein Uhlenbeck processes," Statistical Inference for Stochastic Processes, Springer, vol. 18(1), pages 69-98, April.
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