Ivan Nourdin 
Selected Aspects of Fractional Brownian Motion [PDF ebook] 

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Fractional Brownian motion (f Bm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental importance for financial data and in internet traffic. The mathematical theory of f Bm is currently being developed vigorously by a number of stochastic analysts, in various directions, using complementary and sometimes competing tools. This book is concerned with several aspects of f Bm, including the stochastic integration with respect to it, the study of its supremum and its appearance as limit of partial sums involving stationary sequences, to name but a few. The book is addressed to researchers and graduate students in probability and mathematical statistics. With very few exceptions (where precise references are given), every stated result is proved.

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Table des matières

1. Preliminaries.- 2. Fractional Brownian motion.- 3. Integration with respect to fractional Brownian motion.- 4. Supremum of the fractional Brownian motion.- 5. Malliavin calculus in a nutshell.- 6. Central limit theorem on the Wiener space.- 7. Weak convergence of partial sums of stationary sequences.- 8. Non-commutative fractional Brownian motion.

A propos de l’auteur

Ivan Nourdin is full professor in Mathematics at Université de Lorraine (France). His research interests include Malliavin calculus, Stein’s method and free probability.

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Langue Anglais ● Format PDF ● Pages 124 ● ISBN 9788847028234 ● Taille du fichier 0.9 MB ● Maison d’édition Springer Italia ● Lieu Milano ● Pays IT ● Publié 2013 ● Téléchargeable 24 mois ● Devise EUR ● ID 2651084 ● Protection contre la copie DRM sociale

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