Probability in Banach Spaces: Isoperimetry and Processes

Couverture
Springer Science & Business Media, 1991 - 480 pages

Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.

 

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Table des matières

III
14
IV
15
V
25
VI
30
VII
34
VIII
37
X
43
XI
47
XLVII
245
XLVIII
254
XLIX
269
L
272
LI
273
LII
280
LIII
289
LIV
295

XII
50
XIII
52
XIV
54
XV
56
XVI
64
XVII
73
XVIII
87
XIX
89
XXI
95
XXII
98
XXIII
104
XXIV
111
XXV
120
XXVI
122
XXVII
124
XXVIII
133
XXIX
141
XXX
147
XXXI
149
XXXII
150
XXXIII
155
XXXIV
162
XXXV
176
XXXVI
178
XXXVII
179
XXXVIII
186
XXXIX
195
XL
196
XLII
203
XLIII
216
XLIV
233
XLV
236
XLVI
237
LV
297
LVI
299
LVII
309
LVIII
318
LIX
329
LX
332
LXI
333
LXII
349
LXIII
357
LXIV
363
LXV
365
LXVII
369
LXVIII
382
LXIX
387
LXX
392
LXXI
394
LXXII
395
LXXIII
402
LXXIV
411
LXXV
419
LXXVI
421
LXXVIII
427
LXXIX
430
LXXX
434
LXXXI
438
LXXXII
448
LXXXIII
453
LXXXIV
456
LXXXV
459
LXXXVI
461
LXXXVII
478
Droits d'auteur

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Expressions et termes fréquents

Fréquemment cités

Page 1 - In addition, the law of large numbers and the central limit theorem for sums of identically distributed random variables with finite variance and some ideas on best linear prediction are given. Chapter 9, "Sums of Independent Random Variables" (23 pages), deals with the theory of characteristic functions.
Page 11 - M, we shall study the behaviour in law and as of the fluctuations around these laws of large numbers (central limit theorem and law of the iterated logarithm).

À propos de l'auteur (1991)

Michel Ledoux held first a research position with CNRS, and since 1991 is Professor at the University of Toulouse. He is moreover, since 2010, a senior member of the Institut Universitaire de France, having been also a junior member from 1997 to 2002. He has held associate editor appointments for various journals, including the Annals of Probability and Probability Theory and Related Fields (current). His research interests centre on probability, random matrices, logarithmic Sobolev inequalities, probability in Banach spaces.

Michel Talagrand has held a research position with the CNRS since 1974. His thesis was directed by Gustave Choquet and his interests revolve around the theory of stochastic processes and probability in Banach spaces, as well as the mathematical theory of spin glasses. He was invited to deliver a lecture at the International Congress of Mathematicians in 1990, and to deliver a plenary lecture at the same congress in 1998. He received the Loeve Prize (1995) and the Fermat Prize (1997) for his work in probability theory. He was elected to the Paris Academy of Sciences in 2004.

Informations bibliographiques