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AuthorEmery, Michel. author
TitleLectures on Probability Theory and Statistics [electronic resource] : Ecole d'Etรฉ de Probabilitรฉs de Saint-Flour XXVIII - 1998 / by Michel Emery, Arkadi Nemirovski, Dan Voiculescu ; edited by Pierre Bernard
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2000
Connect tohttp://dx.doi.org/10.1007/BFb0106703
Descript XIII, 349 p. online resource

SUMMARY

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


CONTENT

Variรฉtรฉs, vecteurs, covecteurs, diffuseurs, codiffuseurs -- Semimartingales dans une variรฉtรฉ et gรฉomรฉtrie d'ordre 2 -- Connexions et martingales -- Fonctions convexes et comportement des martingales -- Mouvements browniens et applications harmoniques -- Preface -- Estimating regression functions from Hรถlder balls -- Estimating regression functions from Sobolev balls -- Spatial adaptive estimation on Sobolev balls -- Estimating signals satisfying differential inequalities -- Aggregation of estimates, I -- Aggregation of estimates, II -- Estimating functionals, I -- Estimating functionals, II -- Noncommutative probability and operator algebra background -- Addition of freely independent noncommutative random variables -- Multiplication of freely independent noncommutative random variables -- Generalized canonical form, noncrossing partitions -- Free independence with amalgamation -- Some basic free processes -- Random matrices in the large N limit -- Free entropy


Mathematics Mathematical analysis Analysis (Mathematics) Differential geometry Probabilities Statistics Mathematics Probability Theory and Stochastic Processes Analysis Differential Geometry Statistical Theory and Methods



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