Share

Selected Aspects of Fractional Brownian Motion

2013-01-17 Mathematics
Download Selected Aspects of Fractional Brownian Motion PDF Online Free

Author :
Release : 2013-01-17
Genre : Mathematics
Kind : eBook
Book Rating : 23X/5 ( reviews)

GET EBOOK


Book Synopsis Selected Aspects of Fractional Brownian Motion by : Ivan Nourdin

Download or read book Selected Aspects of Fractional Brownian Motion written by Ivan Nourdin. This book was released on 2013-01-17. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Normal Approximations with Malliavin Calculus

2012-05-10 Mathematics
Download Normal Approximations with Malliavin Calculus PDF Online Free

Author :
Release : 2012-05-10
Genre : Mathematics
Kind : eBook
Book Rating : 777/5 ( reviews)

GET EBOOK


Book Synopsis Normal Approximations with Malliavin Calculus by : Ivan Nourdin

Download or read book Normal Approximations with Malliavin Calculus written by Ivan Nourdin. This book was released on 2012-05-10. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.

Stochastic Calculus for Fractional Brownian Motion and Related Processes

2008-01-02 Mathematics
Download Stochastic Calculus for Fractional Brownian Motion and Related Processes PDF Online Free

Author :
Release : 2008-01-02
Genre : Mathematics
Kind : eBook
Book Rating : 720/5 ( reviews)

GET EBOOK


Book Synopsis Stochastic Calculus for Fractional Brownian Motion and Related Processes by : Yuliya Mishura

Download or read book Stochastic Calculus for Fractional Brownian Motion and Related Processes written by Yuliya Mishura. This book was released on 2008-01-02. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines the theory of fractional Brownian motion and other long-memory processes. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. It proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.

Brownian Motion

2010-03-25 Mathematics
Download Brownian Motion PDF Online Free

Author :
Release : 2010-03-25
Genre : Mathematics
Kind : eBook
Book Rating : 578/5 ( reviews)

GET EBOOK


Book Synopsis Brownian Motion by : Peter Mörters

Download or read book Brownian Motion written by Peter Mörters. This book was released on 2010-03-25. Available in PDF, EPUB and Kindle. Book excerpt: This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.

Fractional Brownian Motion

2019-04-10 Mathematics
Download Fractional Brownian Motion PDF Online Free

Author :
Release : 2019-04-10
Genre : Mathematics
Kind : eBook
Book Rating : 338/5 ( reviews)

GET EBOOK


Book Synopsis Fractional Brownian Motion by : Oksana Banna

Download or read book Fractional Brownian Motion written by Oksana Banna. This book was released on 2019-04-10. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies the relationships between fractional Brownian motion (fBm) and other processes of more simple form. In particular, this book solves the problem of the projection of fBm onto the space of Gaussian martingales that can be represented as Wiener integrals with respect to a Wiener process. It is proved that there exists a unique martingale closest to fBm in the uniform integral norm. Numerical results concerning the approximation problem are given. The upper bounds of distances from fBm to the different subspaces of Gaussian martingales are evaluated and the numerical calculations are involved. The approximations of fBm by a uniformly convergent series of Lebesgue integrals, semimartingales and absolutely continuous processes are presented. As auxiliary but interesting results, the bounds from below and from above for the coefficient appearing in the representation of fBm via the Wiener process are established and some new inequalities for Gamma functions, and even for trigonometric functions, are obtained.

You may also like...