Selfsimilar Processes (Princeton Series in Applied Mathematics)
| Author | : | |
| Rating | : | 4.71 (706 Votes) |
| Asin | : | 0691096279 |
| Format Type | : | paperback |
| Number of Pages | : | 152 Pages |
| Publish Date | : | 2017-12-10 |
| Language | : | English |
DESCRIPTION:
And because this book requires only modest mathematical sophistication, it is accessible to a wide audience."--Gennady Samorodnitsky, Cornell University . From the Inside Flap "Authoritative and written by leading experts, this book is a significant contribution to a growing field. Selfsimilar processes crop up in a wide range of subjects from finance to physics, so this book will have a correspondingly wide readership."--Chris Rogers, Bath University "This is a timely book. Everybody is talking about scaling, and selfsimilar stochastic processes are the basic and the clearest examples of models with scal
Palle E T Jorgensen said Helps to clarify and organize the subject.. Selfsimilar processes are stochastic processes that are invariant in distribution under suitable scaling of time and/or space. Fractional Brownican motion is perhaps the best known of these, and it is used in telecommunication and in stochastic integration. Other m. Proofs and properties, nothing else. Steve Uhlig I doubt the authors have ever analyzed data to understand what self-similarity means. In this book, you'll only find a few proofs and mathematical properties concerning self-similar processes. You won't find anything else unfortunately. If the aim of the authors wa
Makoto Maejima is Professor of Mathematics at Keio University, Yokohama, Japan. . He has published extensively on selfsimilarity and stable processes. He is the author of numerous scientific papers on stochastic processes and their applications and the coauthor of the influential book on "Modelling of Extremal Events for Insurance and Finance". Paul Embrechts is Professor of
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. 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. 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. Numerous references point the reader to current applications. 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. An example of this is the absolute returns of equity data in finance. The modeling of stochastic dependence is fundamental for understanding random systems evolving in time. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that