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On Convergence of the Uniform Norm and Approximation for Stochastic Processes from the Space $${\textbf{F}}_\psi (\Omega )$$ F ψ ( Ω )

Author

Listed:
  • Iryna Rozora

    (Taras Shevchenko National University of Kyiv
    National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”)

  • Yurii Mlavets

    (Uzhhorod National University)

  • Olga Vasylyk

    (National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”)

  • Volodymyr Polishchuk

    (Uzhhorod National University)

Abstract

In this paper, we consider random variables and stochastic processes from the space $${\textbf{F}}_\psi (\Omega )$$ F ψ ( Ω ) and study approximation problems for such processes. The method of series decomposition of a stochastic process from $${\textbf{F}}_\psi (\Omega )$$ F ψ ( Ω ) is used to find an approximating process called a model. The rate of convergence of the model to the process in the uniform norm is investigated. We develop an approach for estimating the cut-off level of the model under given accuracy and reliability of the simulation.

Suggested Citation

  • Iryna Rozora & Yurii Mlavets & Olga Vasylyk & Volodymyr Polishchuk, 2024. "On Convergence of the Uniform Norm and Approximation for Stochastic Processes from the Space $${\textbf{F}}_\psi (\Omega )$$ F ψ ( Ω )," Journal of Theoretical Probability, Springer, vol. 37(2), pages 1627-1653, June.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:2:d:10.1007_s10959-023-01309-x
    DOI: 10.1007/s10959-023-01309-x
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