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

UDC 519.21 We consider nonstationary sequences of <mml:math> <mml:mrow> <mml:mi>φ</mml:mi> </mml:mrow> </mml:math> -mixing random variables. By using the Levy–Prokhorov distance, we estimate the rate of convergence in the invariance principle for nonstationary <mml:math> <mml:mrow> <mml:mi>φ</mml:mi> </mml:mrow> </mml:math> -mixing random variables. The obtained results extend and generalize several known results for nonstationary <mml:math> <mml:mrow> <mml:mi>φ</mml:mi> </mml:mrow> </mml:math> -mixing random variables.

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