Asymptotic Properties of Permanental Sequences: Related to Birth and Death Processes and Autoregressive Gaussian Sequences

Marcus, Michael B./ Rosen, Jay

ISBN 10: 3030694844 / ISBN 13: 9783030694845

Verlag: Springer Nature, 2021

Beschreibung

128 pages. 9.25x6.10x0.35 inches. In Stock.

Bestandsnummer des Verkäufers x-3030694844

Bibliografische Details

• Titel: Asymptotic Properties of Permanental Sequences: Related to Birth and Death Processes and Autoregressive Gaussian Sequences
• Verlag: Springer Nature
• Erscheinungsjahr: 2021
• Sprache: Englisch
• ISBN-10: 3030694844
• ISBN-13: 9783030694845
• Einband: Paperback
• Zustand: Brand New
• Gewicht: 0,2 Kilogramm

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

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.