Selfsimilar Processes

Nonfiction, Science & Nature, Mathematics, Probability, Statistics
Cover of the book Selfsimilar Processes by Paul Embrechts, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Paul Embrechts ISBN: 9781400825103
Publisher: Princeton University Press Publication: January 10, 2009
Imprint: Princeton University Press Language: English
Author: Paul Embrechts
ISBN: 9781400825103
Publisher: Princeton University Press
Publication: January 10, 2009
Imprint: Princeton University Press
Language: English

The modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications.

After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications.

Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

The modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications.

After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications.

Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity.

More books from Princeton University Press

Cover of the book The Best Writing on Mathematics 2011 by Paul Embrechts
Cover of the book An Academic Life by Paul Embrechts
Cover of the book Founding Gods, Inventing Nations by Paul Embrechts
Cover of the book California Greenin' by Paul Embrechts
Cover of the book The Subprime Solution by Paul Embrechts
Cover of the book Revolutions in Sovereignty by Paul Embrechts
Cover of the book The Tyranny of Guilt by Paul Embrechts
Cover of the book Hamas and Civil Society in Gaza by Paul Embrechts
Cover of the book The Ethics of Identity by Paul Embrechts
Cover of the book Regulating Aversion by Paul Embrechts
Cover of the book Heart of Darkness by Paul Embrechts
Cover of the book Financing the American Dream by Paul Embrechts
Cover of the book The Eternal City by Paul Embrechts
Cover of the book Economic Gangsters by Paul Embrechts
Cover of the book Getting Respect by Paul Embrechts
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy