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Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with Applications

Author

Listed:
  • Nikolaos Limnios

    (Sorbonne University Alliance, Université de Technologie de Compiègne, 60203 Compiègne, France)

  • Anatoliy Swishchuk

    (Department of Mathematics and Statistics, Faculty of Science, University of Calgary, Calgary, AB T2N 1N4, Canada)

Abstract

This paper deals with discrete-time semi-Markov random evolutions (DTSMRE) in reduced random media. The reduction can be done for ergodic and non ergodic media. Asymptotic approximations of random evolutions living in reducible random media (random environment) are obtained. Namely, averaging, diffusion approximation and normal deviation or diffusion approximation with equilibrium by martingale weak convergence method are obtained. Applications of the above results to the additive functionals and dynamical systems in discrete-time produce the above tree types of asymptotic results.

Suggested Citation

  • Nikolaos Limnios & Anatoliy Swishchuk, 2020. "Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with Applications," Mathematics, MDPI, vol. 8(6), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:963-:d:370485
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    References listed on IDEAS

    as
    1. Yang, Jen-Wei & Tsai, Shu-Yu & Shyu, So-De & Chang, Chia-Chien, 2016. "Pairs trading: The performance of a stochastic spread model with regime switching-evidence from the S&P 500," International Review of Economics & Finance, Elsevier, vol. 43(C), pages 139-150.
    2. Touchette, Hugo, 2018. "Introduction to dynamical large deviations of Markov processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 504(C), pages 5-19.
    3. Anatoliy Swishchuk & M. Shafiqul Islam, 2010. "Diffusion Approximations of the Geometric Markov Renewal Processes and Option Price Formulas," International Journal of Stochastic Analysis, Hindawi, vol. 2010, pages 1-21, December.
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