This book was first published in 2006. Written by two of the foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum and then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original, readable book will appeal to both researchers and advanced graduate students.

Markov Processes, Gaussian Processes, and Local Times (Cambridge Studies in Advanced Mathematics)

Science & Math

Marcus, Michael B.

Rosen, Jay

Mathematics

Cambridge University Press

Written by two foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and for experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum, then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original, readable book will appeal to both researchers and advanced graduate students.

Markov Processes, Gaussian Processes, and Local Times (Cambridge Studies in Advanced Mathematics, Series Number 100)

Random Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101 (Annals of Mathematics Studies, 101)

In this book the authors give the first necessary and sufficient conditions for the uniform convergence a.s. of random Fourier series on locally compact Abelian groups and on compact non-Abelian groups. They also obtain many related results. For example, whenever a random Fourier series converges uniformly a.s. it also satisfies the central limit theorem. The methods developed are used to study some questions in harmonic analysis that are not intrinsically random. For example, a new characterization of Sidon sets is derived.The major results depend heavily on the Dudley-Fernique necessary and sufficient condition for the continuity of stationary Gaussian processes and on recent work on sums of independent Banach space valued random variables. It is noteworthy that the proofs for the Abelian case immediately extend to the non-Abelian case once the proper definition of random Fourier series is made. In doing this the authors obtain new results on sums of independent random matrices with elements in a Banach space. The final chapter of the book suggests several directions for further research.

Random Fourier Series with Applications to Harmonic Analysis (Annals of Mathematics Studies)

Pisier, Gilles

Princeton University Press

In a series of three papers published in 1930 and 1931, Paley and Zygmund 44 studied a variety of problems concerning series of independent random functions and raised the question of the uniform convergence a.s. of the random Fourier series.

Xe-Radial Processes and Random Fourier Series (Memoirs of the American Mathematical Society)

Amer Mathematical Society

Written by two foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and for experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum, then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original, readable book will appeal to both researchers and advanced graduate students.

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.

Asymptotic Properties of Permanental Sequences: Related to Birth and Death Processes and Autoregressive Gaussian Sequences (SpringerBriefs in Probability and Mathematical Statistics)

Springer

See the best price to sell, buy, or rent books by Marcus, Michael B.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Marcus, Michael B.

See the best price to sell, buy, or rent books by Marcus, Michael B.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Markov Processes, Gaussian Processes, and Local Times (Cambridge Studies in Advanced Mathematics)

Markov Processes, Gaussian Processes, and Local Times (Cambridge Studies in Advanced Mathematics, Series Number 100)

Random Fourier Series with Applications to Harmonic Analysis (Annals of Mathematics Studies)

Random Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101 (Annals of Mathematics Studies, 101)

Xe-Radial Processes and Random Fourier Series (Memoirs of the American Mathematical Society)

Markov Processes, Gaussian Processes, and Local Times (Cambridge Studies in Advanced Mathematics, Series Number 100)

Asymptotic Properties of Permanental Sequences: Related to Birth and Death Processes and Autoregressive Gaussian Sequences (SpringerBriefs in Probability and Mathematical Statistics)