发帖
雷达卡
Publication Date: January 17, 2013
Fractional Brownian motion (fBm) 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 fBm 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 fBm, 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.
本帖隐藏的内容
004_Selected Aspects of Fractional Brownian Motion.pdf
(3.05 MB, 需要: 10 个论坛币)
Editorial ReviewsReview
From the reviews:
“This short monograph by Ivan Nourdin deals with several aspects of fractional Brownian motion (fBm) ranging from basic properties over integration theory to non-commutative fractional Brownian motion. … The text is well written and almost all results are given with complete proofs. It is certainly a valuable contribution to the literature on fBm and will be a helpful source for everybody interested in new developments on fBm and its relation to other fields.” (Hilmar Mai, zbMATH, Vol. 1274, 2013)
From the Back Cover
Fractional Brownian motion (fBm) 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 fBm 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 fBm, 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.
About the Author
Ivan Nourdin is full professor in Mathematics at Université de Lorraine (France). His research interests include Malliavin calculus, Stein's method and free probability.
Product Details
- File Size: 3832 KB
- Print Length: 122 pages
- Publisher: Springer Milan; 1 edition (January 17, 2013)
- Publication Date: January 17, 2013
- Language: English
- ASIN: B00BLR498U
[size=1.2em]
提升卡
置顶卡
沉默卡
变色卡
抢沙发
千斤顶
显身卡
京公网安备 11010802022788号
