Selfsimilar Processes (Princeton Series in Applied Mathematics)

You looking to find the "Selfsimilar Processes (Princeton Series in Applied Mathematics)" Good news! You can purchase Selfsimilar Processes (Princeton Series in Applied Mathematics) with secure price and compare to view update price on this product. And deals on this product is available only for limited time.

   

Product Description

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.

</p>

Selfsimilar Processes (Princeton Series in Applied Mathematics) Review

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 more recent aplications include finance.

While the underlying idea behind all of this is quite simple and can be traced back to Kolmogorov, it is only recently, with the advent of wavelet methods, that the *computational* power has come into focus.

At the same time, this connection to wavelet analysis is now bringing the *Hilbert space theoretic features* of the subject back to the fore. Amusingly, this was in fact a dominant feature which motivated both A. N. Kolmogorov and Norbert Wiener in the early days; e.g., curves in Hilbert space.

I was pleased with this lovely little book, as it brings out beautifully these two aspects of the subject; and I expect that the book will go over well in the classroom. And the book should help bridge mathematical analysis, probability, and applications.

Reviewed by Palle Jorgensen, September 2004.

Most of the consumer Reviews tell that the "Selfsimilar Processes (Princeton Series in Applied Mathematics)" are high quality item. You can read each testimony from consumers to find out cons and pros from Selfsimilar Processes (Princeton Series in Applied Mathematics) ...