Asymptotic Properties of Permanental Sequences
Related to Birth and Death Processes and Autoregressive Gaussian Sequences
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Beschreibung
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.
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
Autor*in
Michael B. Marcus
Themen in »Asymptotic Properties of Permanental Sequences«
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