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MSC 2000: 46L10, 46L53
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This volume contains lectures given at the Saint-Flour Summer School of Probability Theory during 17th Aug. - 3rd Sept. 1998. The contents of the three courses are the following: - Continuous martingales on differential manifolds. - Topics in non-parametric statistics. - Free probability theory. The reader is expected to have a graduate level in probability theory and statistics. This book is of interest to PhD students in probability and statistics or operators theory as well as for researchers in all these fields. The series of lecture notes from the Saint-Flour Probability Summer School can be considered as an encyclopedia of probability theory and related fields.
Title of the first 10 volumes of the series is Germans to America : lists of passengers arriving at U.S. ports 1850-1855.
The field of stochastic processes is essentially a branch of probability theory, treating probabilistic models that evolve in time. It is best viewed as a branch of mathematics, starting with the axioms of probability and containing a rich and fascinating set of results following from those axioms. Although the results are applicable to many areas, they are best understood initially in terms of their mathematical structure and interrelationships. Applying axiomatic probability results to a real-world area requires creating a probability model for the given area. Stochastic processes were first studied rigorously in the late 19th century to aid in understanding financial markets and Brownian ...