Large Deviations for Discrete-Time Processes with Averaging

Description

Based on the Cramer-Chernoff theorem, which deals with the "rough" logarithmic asymptotics of the distribution of sums of independent, identically random variables, this work primarily approaches the extensions of this theory to dependent and, in particular, non-Markovian cases on function spaces. Recurrent algorithms of identification and adaptive control form the main examples behind the large deviation problems in this volume. The first part of the book exploits some ideas and concepts of the martingale approach, especially the concept of the stochastic exponential. The second part covers Freidlin's approach, based on the Frobenius-type theorems for positive operators, whuch prove to be effective for the cases in consideration. The book should be of value and interest to scientists in the field of probability, statistics and electrical engineering, as well as physicists dealing with statistical mechanics