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.
General
Imprint: |
Springer Nature Switzerland AG
|
Country of origin: |
Switzerland |
Series: |
SpringerBriefs in Probability and Mathematical Statistics |
Release date: |
March 2021 |
First published: |
2021 |
Authors: |
Michael B. Marcus
• Jay Rosen
|
Dimensions: |
235 x 155mm (L x W) |
Format: |
Paperback
|
Pages: |
114 |
Edition: |
1st ed. 2021 |
ISBN-13: |
978-3-03-069484-5 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Probability & statistics
|
LSN: |
3-03-069484-4 |
Barcode: |
9783030694845 |
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