Weak convergence of stochastic processes from spaces $F_\psi(\Omega)$

  • Yurii Yuriiovych Mlavets Uzhhorod National University
  • Yurii Vasylovych Kozachenko Taras Shevchenko National University of Kyiv
  • Nataliia Vasylivna Yurchenko Uzhhorod National University
Keywords: weak convergence, quasi-metric space, $K_\sigma$-space, $\mathbf{F}_\psi(\Omega)$ space, majorant characteristic, metric massiveness, condition $\mathbf{H}$, stochastic processes, Monte Carlo method


This paper is devoted to the investigation of conditions for the  eak convergence in the space $C(T)$ of the stochastic processes from the space $\mathbf{F}_\psi(\Omega)$. Using this conditions the limit theorem for stochastic processes from the space $\mathbf{F}_\psi(\Omega)$ has been obtained. This theorem can be utilized  for gaining the given approximation accuracy  and reliability of integrals depending on parameter by Monte Carlo method.

Author Biographies

Yurii Yuriiovych Mlavets, Uzhhorod National University
Department of Cybernetics and Applied Mathematics, associate professor
Yurii Vasylovych Kozachenko, Taras Shevchenko National University of Kyiv
Department of Probability Theory, Statistics and Actuarial Mathematics, professor
Nataliia Vasylivna Yurchenko, Uzhhorod National University
Department of Algebra, associate professor


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How to Cite
Mlavets, Y. Y., Kozachenko, Y. V., & Yurchenko, N. V. (2018). Weak convergence of stochastic processes from spaces $F_\psi(\Omega)$. Statistics, Optimization & Information Computing, 6(2), 266-277. https://doi.org/10.19139/soic.v6i2.394
Research Articles