An Isospectral Family of Random Processes: January, 1960 (Classic Reprint)
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 17.22
Quantity: Over 20 available
Add to basketItem description from seller
Print on Demand. This book explores the concept of creating a family of non-Gaussian random step functions, all sharing the same power spectrum, that converge to the Gaussian process with the same spectrum as the number of members in the family becomes very large. The author illustrates how to calculate the multivariate distribution of processes and shows how a constructed univariate entropy can serve as an indicator of the extent to which the family has approached the Gaussian limit. The author's findings give insight into the inadequacy of correlation functions and power spectra as a means of characterizing random processes and emphasize the need for higher-order statistics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.
Seller Inventory # 9781332145607_0
- Title
- An Isospectral Family of Random Processes: January, 1960 (Classic Reprint)
- Author
- R. A. Silverman
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1332145604
- ISBN 13
- 9781332145607
- Seller catalogs
- Minutes and Reports
A bridge between non-Gaussian models and Gaussian behavior
This work presents an infinite family of random processes that share the same correlation function, yet are non-Gaussian for most values of a key parameter. The construction starts from a shot-noise (Poisson) process and builds a stationary, random step function whose features can be calculated in principle. As the parameter grows, the processes gradually resemble a Gaussian process with the same power spectrum, highlighting the limits of using only second-order statistics to characterize randomness.
The approach lets you see how higher-order statistics matter in practice and how a single spectrum can correspond to many different stochastic behaviors. By specifying shot timings and rectangular shot shapes, the author shows how to derive univariate and multivariate distributions, and how sample functions look under different shot-density regimes. The results are grounded in a familiar method, yet give a complete, theory-backed view of a clearly non-Gaussian family that transitions toward Gaussianity.- Learn how a stationary shot-noise construction yields an isospectral family of processes
- See the relationship between correlation functions, power spectra, and higher-order statistics
- Discover how non-Gaussian models converge to Gaussian behavior as a parameter changes
- Explore visual examples illustrating low, medium, and high shot-density cases
"Synopsis" may belong to another edition of this title.
Forgotten Books
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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