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Large Deviations and Idempotent Probability (Paperback)
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Large Deviations and Idempotent Probability (Paperback)
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In the view of many probabilists, author Anatolii Puhalskii's
research results stand among the most significant achievements in
the modern theory of large deviations. In fact, his work marked a
turning point in the depth of our understanding of the connections
between the large deviation principle (LDP) and well-known methods
for establishing weak convergence results. Large Deviations and
Idempotent Probability expounds upon the recent methodology of
building large deviation theory along the lines of weak convergence
theory. The author develops an idempotent (or maxitive) probability
theory, introduces idempotent analogues of martingales
(maxingales), Wiener and Poisson processes, and Ito differential
equations, and studies their properties. The large deviation
principle for stochastic processes is formulated as a certain type
of convergence of stochastic processes to idempotent processes. The
author calls this large deviation convergence. The approach to
establishing large deviation convergence uses novel compactness
arguments. Coupled with the power of stochastic calculus, this
leads to very general results on large deviation asymptotics of
semimartingales. Large and moderate deviation asymptotics are
treated in a unified manner. Starting with the foundations of
idempotent measure theory and culminating in applications to large
deviation asymptotics of queueing systems, Large Deviations and
Idempotent Probability offers an outstanding opportunity to examine
both the development of a remarkable approach and recently
discovered results as presented by one of the foremost leaders in
the field.
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