Authors:
- Is the first monograph that addresses permanental processes, a new class of stochastic processes
- Employs a novel approach to obtain the precise asymptotic behavior at infinity of a large class of permanental sequences related to birth and death processes and autoregressive Gaussian sequences
- Appeals to researchers and advanced graduate students
Part of the book series: SpringerBriefs in Probability and Mathematical Statistics (SBPMS)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
About this book
This SpringerBriefs employs a novel approach to obtain the precise asymptotic behavior at infinity of a large class of permanental sequences related to birth and death processes and autoregressive Gaussian sequences using techniques from the theory of Gaussian processes and Markov chains.
The authors study alpha-permanental processes that are positive infinitely divisible processes determined by the potential density of a transient Markov process. When the Markov process is symmetric, a 1/2-permanental process is the square of a Gaussian process. Permanental processes are related by the Dynkin isomorphism theorem to the total accumulated local time of the Markov process when the potential density is symmetric, and by a generalization of the Dynkin theorem by Eisenbaum and Kaspi without requiring symmetry. Permanental processes are also related to chi square processes and loop soups.The book appeals to researchers and advanced graduate students interested in stochastic processes, infinitely divisible processes and Markov chains.
Authors and Affiliations
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New York, USA
Michael B. Marcus
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Department of Mathematics, College of Staten Island, City University of New York, Staten Island, USA
Jay Rosen
About the authors
Professor Marcus is Professor Emeritus at The City College, CUNY and the CUNY Graduate Center and Professor Rosen is Distinguished Professor at The College of Staten Island, CUNY and the CUNY Graduate Center. Together they have published more than two hundred papers of which thirty six were written jointly and five books three of which were written jointly. Together they have delivered more than three hundred invited talks. Their research is on sample path properties of stochastic processes, specializing in Gaussian processes, random Fourier series, Gaussian chaos, Levy processes, Markov processes, local times, intersection local times, loop soups and permanental processes.
Bibliographic Information
Book Title: Asymptotic Properties of Permanental Sequences
Book Subtitle: Related to Birth and Death Processes and Autoregressive Gaussian Sequences
Authors: Michael B. Marcus, Jay Rosen
Series Title: SpringerBriefs in Probability and Mathematical Statistics
DOI: https://doi.org/10.1007/978-3-030-69485-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Softcover ISBN: 978-3-030-69484-5Published: 31 March 2021
eBook ISBN: 978-3-030-69485-2Published: 30 March 2021
Series ISSN: 2365-4333
Series E-ISSN: 2365-4341
Edition Number: 1
Number of Pages: XI, 114
Number of Illustrations: 1 b/w illustrations, 1 illustrations in colour