We extend some sharp inequalities for martingale-differences to general multiplicative systems of random variables. The key ingredient in the proofs is a technique reducing case Rademacher variables without change constants inequalities.

This paper deals with maximum likelihood and least square segmentation of autoregressive random sequences with abruptly changing parameters. Conditional distribution of the observations has been derived. Objective function was modified to the form suitable to apply dynamic programming method for its optimization. Expressions of Bellman functions for this case were obtained. Performance of prese...