On the rate of convergence in the invariance principle for real-valued functions of Doeblin processes (Q799299)

Using Prokhorov's metric it is shown that under suitable conditions the rate of convergence in the functional central limit theorem for C-valued partial sum processes based on real-valued functions of stationary Markov processes satisfying Doeblin's condition is \(O(n^{-\delta /3+2\delta})\) for \(0<\delta <3/2\). A non-uniform Berry-Esseen estimate for the maximum absolute value of partial sums of bounded functions is also established.