This book is mainly based on the Cramir--Chernoff renowned theorem,
which deals with the 'rough' logarithmic asymptotics of the
distribution of sums of independent, identically distributed random
variables. The authors approach primarily the extensions of this
theory to dependent, and in particular, nonmarkovian 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 of the book
covers Freindlin's approach, based on the Frobenius-type theorems
for positive operators, which prove to be effective for the cases
in consideration.
General
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