Title :
Martingales and information divergence
Author :
Harremoës, Peter
Author_Institution :
Dept. of Math., Copenhagen Univ.
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
Keywords :
convergence; information theory; stochastic processes; Markov chains; Shannon-McMillan-Breiman theorem; ergodic sequences; information divergence; maximal inequality; nonnegative martingales; pointwise convergence; Convergence; Councils; Entropy; Information theory; Probability distribution; Q measurement; State-space methods; Topology;
Conference_Titel :
Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on
Conference_Location :
Adelaide, SA
Print_ISBN :
0-7803-9151-9
DOI :
10.1109/ISIT.2005.1523315
