Abstract:
A new maximal inequality for non-negative martingales is proved. It strengthens a well-known maximal inequality by Doob, and it is demonstrated that the stated inequality...Show MoreMetadata
Abstract:
A new maximal inequality for non-negative martingales is proved. It strengthens a well-known maximal inequality by Doob, and it is demonstrated that the stated inequality is tight. The inequality emphasizes the relation between martingales and information divergence. It implies pointwise convergence of X log X bounded martingales. A similar inequality holds for ergodic sequences. Relations to the Shannon-McMillan-Breiman theorem and Markov chains are mentioned
Date of Conference: 04-09 September 2005
Date Added to IEEE Xplore: 31 October 2005
Print ISBN:0-7803-9151-9