Abstract
The authors study approximation to the partial sum processes which is based on the stationary sequences of random variables having the structure of the so-called moving averages of independent identically distributed observations. In particular, the rates of convergence both in Donsker's and Strassen's invariance principles are obtained in the case when the limit Gaussian process is a fractional Brownian motion with an arbitrary Hurst parameter.
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Arkashov, N.S., Borisov, I.S. Gaussian Approximation to the Partial Sum Processes of Moving Averages. Siberian Mathematical Journal 45, 1000–1030 (2004). https://doi.org/10.1023/B:SIMJ.0000048916.15922.b4
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DOI: https://doi.org/10.1023/B:SIMJ.0000048916.15922.b4