On the rate of convergence in the invariance principle for weakly dependent random variables

A. K.  Mukhamedov

doi:10.37863/umzh.v74i9.6244

A. K. Mukhamedov Nat. Univ. Uzbekistan, Tashkent

DOI: https://doi.org/10.37863/umzh.v74i9.6244

Keywords: uniformly strong mixing random variables, the rate of convergence, an invariance principle.

Abstract

UDC 519.21

We consider nonstationary sequences of $\varphi$-mixing random variables. By using the Levy–Prokhorov distance, we estimate the rate of convergence in the invariance principle for nonstationary $\varphi$-mixing random variables. The obtained results extend and generalize several known results for nonstationary $\varphi$-mixing random variables.

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