On Borovkov's estimate in the Invariance Principle

The first general estimate in the functional CLT (i.e. in the Invariance Principle) was obtained by A. Borovkov in 1973 in terms of the Lyapunov fractions of order not greater than three. Here we present explicit numerical bounds for the constants in Borovkov's estimate. In addition, we have found similar but more precise estimates in terms of truncated Lyapunov fractions.