Includes bibliographical references (p. -320) and index.
|Statement||Francesca Biagini ... [et al.].|
|Series||Probability and its applications|
|LC Classifications||QA274.2 .S7725 2008|
|The Physical Object|
|Pagination||xii, 329 p. ;|
|Number of Pages||329|
|ISBN 10||1852339969, 1846287979|
|ISBN 10||9781852339968, 9781846287978|
|LC Control Number||2008920683|
This huge range of potential applications makes fBm an interesting object of study. fBm represents a natural one-parameter extension of classical Brownian motion therefore it is natural to ask if a stochastic calculus for fBm can be developed. The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this by: Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This huge range of potential applications makes fBm an interesting object of study. Several approaches have been used to develop the concept of stochastic calculus for. Intrinsic properties of the fractional Brownian motion.- Stochastic calculus.- Wiener and divergence-type integrals for fractional Brownian motion.- Fractional Wick Ito Skorohod (fWIS) integrals for fBm of Hurst index H >1/ WickIto Skorohod (WIS) integrals for fractional Brownian motion.- Pathwise integrals for fractional Brownian motion
Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. Introductory comments This is an introduction to stochastic calculus. I will assume that the reader has had a post-calculus course in probability or Size: KB. Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Get this from a library! Stochastic calculus for fractional Brownian motion and applications. [Francesca Biagini;] -- "Several approaches have been used to develop the concept of stochastic calculus for fBm. The purpose of this book is to present a comprehensive account of the different definitions of stochastic.
Stochastic calculus for fractional Brownian motion and applications Francesca Biagini, Yaozhong Hu, Bernt Øksendal, Tusheng Zhang (auth.) Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. In this paper a stochastic calculus is given for the fractional Brownian motions that have the Hurst parameter in (1/2, 1). A stochastic integral of Ito type is defined for a family of integrands. Stochastic Calculus for Fractional Brownian Motion and Applications by Francesca Biagini, , available at Book Depository with free delivery worldwide.5/5(1). Stochastic calculus is a branch of mathematics that operates on stochastic allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly. The best-known stochastic process to which stochastic calculus is applied is the Wiener process (named in .