Integration and probability

Paul Malliavin - Collection Graduate Texts in Mathematics

332 pages, parution le 15/01/1995

Ajouter à une liste

Indisponible

Résumé

This book is designed to be an introduction to analysis with the proper mix of abstract theories and concrete problems. It starts with general measure theory, treats Borel and Radon measures (with particular attention paid to Lebesgue measure) and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the Fourier analysis of such. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution to the existing literature gives the reader a taste of the fact that analysis is not a collection of independent theories but can be treated as a whole.

The book can serve as a text for a first year graduate course in real analysis. It includes a large number of illuminating exercises by Gerard Letac. Instructive and detailed solutions can be found in "Exercises and Solutions Manual for Integration and Probability" by Gerard Letac, Springer-Verlag, 1995. The upcoming book "Stochastic Analysis" by Paul Malliavin, Grundlehren der Mathematischen Wissenschaften, Volume 313, Springer-Verlag, 1995, is meant for second year graduate students who are planning to continue their studies in probability theory.

Sommaire

Measurable spaces and integrable functions
Borel measures and radon measures
Fourier analysis
Hilbert space method and limit theorems in probability theory
Gaussian Sobolev spaces ans stochastic calculus of variations

Voir tout

Replier

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Paul Malliavin
Collection	Graduate Texts in Mathematics
Parution	15/01/1995
Nb. de pages	332
Format	16 x 24
Couverture	Relié
Poids	636g
Intérieur	Noir et Blanc
EAN13	9780387944098
ISBN13	978-0-387-94409-8