Abstract:
We obtain estimates for the accuracy with which a random broken line constructed from sums of independent nonidentically distributed random variables can be approximated by a Wiener process. All estimates depend explicitly on the moments of the random variables; meanwhile, these moments can be of a rather general form. In the case of identically distributed random variables we succeed for the first time in constructing an estimate depending explicitly on the common distribution of the summands and directly implying all results of the famous articles by Komlós, Major, and Tusnády which are devoted to estimates in the invariance principle.
Keywords:invariance principle, estimates for the rate of convergence, Komlós–Major–Tusnády estimates, method of the same probability space.
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