The book introduces classical inequalities in vector and functional
spaces with applications to probability. It develops new analytical
inequalities, with sharper bounds and generalizations to the sum or
the supremum of random variables, to martingales, to transformed
Brownian motions and diffusions, to Markov and point processes,
renewal, branching and shock processes.In this third edition, the
inequalities for martingales are presented in two chapters for
discrete and time-continuous local martingales with new results for
the bound of the norms of a martingale by the norms of the
predictable processes of its quadratic variations, for the norms of
their supremum and their p-variations. More inequalities are also
covered for the tail probabilities of Gaussian processes and for
spatial processes.This book is well-suited for undergraduate and
graduate students as well as researchers in theoretical and applied
mathematics.
General
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