On Borovkov's estimate in the Invariance Principle

摘要

The first general estimate in the functional CLT (i.e. in theInvariance Principle) was obtained by A. Borovkov in 1973 in terms ofthe Lyapunov fractions of order not greater than three. Here we presentexplicit numerical bounds for the constants in Borovkov’s estimate. Inaddition, we have found similar but more precise estimates in terms oftruncated Lyapunov fractions.