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Asymptotic Properties of Permanental Sequences

Related to Birth and Death Processes and Autoregressive Gaussian Sequences

  • 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

  • 1743 Accesses

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
  2. Introduction

    • Michael B. Marcus, Jay Rosen
    Pages 1-17
  3. Birth and Death Processes

    • Michael B. Marcus, Jay Rosen
    Pages 19-32
  4. Birth and Death Processes with Emigration

    • Michael B. Marcus, Jay Rosen
    Pages 33-45
  5. Relating Permanental Sequences to Gaussian Sequences

    • Michael B. Marcus, Jay Rosen
    Pages 87-96
  6. Uniform Markov Chains

    • Michael B. Marcus, Jay Rosen
    Pages 103-110
  7. Back Matter

    Pages 111-114

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.

Keywords

  • autoregressive Gaussian sequences
  • birth and death processes
  • properties of permanental sequences
  • uniform Markov chains
  • time-varying processes
  • 60E07, 60G15, 60G17, 60G99, 60J27
  • asymptotic limits of stochastic processes
  • infinitely divisible processes
  • Q-matrices

Authors and Affiliations

  • New York, USA

    Michael B. Marcus

  • 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 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

  • Topics: Probability Theory and Stochastic Processes

Buy it now

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access