# Lectures on probability theory and statistics : Ecole d'été de probabilités de Saint-Flour XXVIII, 1998 / M. Emery, A. Nemirovski, D. Voiculescu ; editor, Pierre Bernard.

##### By: (28th : Ecole d'été de probabilités de Saint-Flour (28th : 1998)

##### Contributor(s): Emery, Michel | Nemirovskiĭ, A. S. (Arkadiĭ Semenovich) | Voiculescu, D. V. (Dan V.) | Bernard, P. (Pierre)

Material type: TextSeries: Lecture notes in mathematics (Springer-Verlag): 1738.Publisher: Berlin ; New York : Springer, ©2000Description: 1 online resource (xi, 349 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540450290; 3540450297Subject(s): Probabilities -- Congresses | Mathematical statistics -- Congresses | Mathematical statistics | Probabilities | Waarschijnlijkheidstheorie | Statistiek | Niet-commutatieve structuren | Probabilidade (estatistica)Genre/Form: Electronic books. | Conference papers and proceedings. Additional physical formats: Print version:: Lectures on probability theory and statistics.DDC classification: 519.2 LOC classification: QA3 | .L28 no.1738Online resources: Click here to access onlineItem type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
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"Lectures given at the Saint-Flour Summer School of Probability Theory during the period 17th August - 3rd September, 1998"--Introduction.

Includes bibliographical references.

Martingales continues dans les variets differentiables. Introduction -- Varit, vecteurs, covecteurs, diffuseurs, codiffuseurs -- Semimartingales dans une varit et gomtrie d'ordre 2 -- Connections et martingales -- Fonctions convexes et comportement des martingales -- Mouvements browniens et applications harmoniques. Topics in Non-Parametric Statistics -- Estimating regression functions from Hlder balls and from Sobolev balls -- Spatial adaptive estimation on Sobolev balls -- Estimating signals satisfying differential inequalities -- Aggregation of estimates I, II -- Estimating functionals I, II. Lectures on Free Probability Theory -- Introduction -- Noncommutative probability and operator algebra background -- Addition and multiplication of freely independent noncommutative random variables -- Multiplication variables -- Generalized canonical form, noncrossing partitions. Free independence with amalgamation -- Some basic free processes -- Random matrices in the large N limit -- Free entropy.

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.

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