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Diffusion Process with Evolution and its Parameter Estimation

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Abstract

A discrete Markov process in an asymptotic diffusion environment with a uniformly ergodic embedded Markov chain can be approximated by an Ornstein–Uhlenbeck process with evolution. The drift parameter estimation is obtained using the stationarity of the Gaussian limit process.

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References

  1. D. Koroliouk, “Binary statistical experiments with persistent nonlinear regression,” Theor. Probability and Math. Statist., Vol. 91, 71–80 (2015).

    Article  MathSciNet  Google Scholar 

  2. Yu. V. Borovskikh and V. S. Korolyuk, Martingale Approximation, VSP, Utrecht (1997).

    Book  Google Scholar 

  3. S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence, Willey, Hoboken (1986).

    Book  Google Scholar 

  4. V. S. Koroliuk and N. Limnios, Stochastic Systems in Merging Phase Space, World Scientific, New Jersey–London (2005).

    Book  Google Scholar 

  5. V. S. Korolyuk and D. Koroliouk, “Diffusion approximation of stochastic Markov models with persistent regression,” Ukrain. Matem. Zhurn., Vol. 47, No. 7, 928–935 (1995).

    MathSciNet  MATH  Google Scholar 

  6. D. Koroliouk, “Stationary statistical experiments and the optimal estimator for a predictable component,” J. of Mathematical Sciences, Vol. 214, No. 2, 20–228 (2016).

    Article  MathSciNet  Google Scholar 

  7. S. N. Cohen and R. J. Elliott, Stochastic Calculus and Applications. Probabilitity and its Application, Birkhauser, Basel (2015).

    Book  Google Scholar 

  8. M. Bel Hadj Khlifa, Yu. Mishura, K. Ralchenko, G. Shevchenko, and M. Zili, “Stochastic differential equations with generalized stochastic volatility and statistical estimators,” Teoriya Imovirnostei ta Matematychna Statystyka, Vol. 96, 8–20 (2017).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. S. Koroliuk

  2. Institute of Telecommunications and Global Information Space, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    D. Koroliouk & S. O. Dovgyi

Authors
  1. V. S. Koroliuk
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  2. D. Koroliouk
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  3. S. O. Dovgyi
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Corresponding author

Correspondence to D. Koroliouk.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2020, pp. 55–62.

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Koroliuk, V.S., Koroliouk, D. & Dovgyi, S.O. Diffusion Process with Evolution and its Parameter Estimation. Cybern Syst Anal 56, 732–738 (2020). https://doi.org/10.1007/s10559-020-00293-y

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  • DOI: https://doi.org/10.1007/s10559-020-00293-y

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