Asymptotic properties of permanental sequence : related to birth and death processes and autoregressive Gaussian sequences / Michael B. Marcus, Jay Rosen.

Format:

Book

Author/Creator:

Rosen, Jay, 1948- author.

Series:

Springer briefs in probability and mathematical statistics.

Springer briefs in probability and mathematical statistics

Language:

English

Subjects (All):

Birth and death processes (Stochastic processes).

Gaussian distribution.

Physical Description:

1 online resource (xi, 114 pages).

Place of Publication:

Cham, Switzerland : Springer, [2021]

Summary:

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.

Contents:

Intro

Preface

Contents

1 Introduction

1.1 General Results

1.2 Applications

2 Birth and Death Processes

3 Birth and Death Processes with Emigration

4 Birth and Death Processes with Emigration Related to First Order Gaussian Autoregressive Sequences

5 Markov Chains with Potentials That Are the Covariances of Higher Order Gaussian Autoregressive Sequences

6 Relating Permanental Sequences to Gaussian Sequences

7 Permanental Sequences with Kernels That Have Uniformly Bounded Row Sums

8 Uniform Markov Chains

Appendix Bibliography

Index.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

3-030-69485-2

OCLC:

1244620227