Robert Azencott's Books

Series of Irregular Observations

Forecasting and Model Building

By: Robert Azencott,Didier Dacunha-Castelle

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Series of Irregular Observations

Forecasting and Model Building

By: Robert Azencott,Didier Dacunha-Castelle

At the university level, in probability and statistics departments or electrical engineering departments, this book contains enough material for a graduate course, or even for an upper-level undergraduate course if the asymptotic studies are reduced to a minimum. The prerequisites for most of the chapters (l - 12) are fairly limited: the elements of Hilbert space theory, and the basics of axiomatic probability theory including L 2-spaces, the notions of distributions, random variables and bounded measures. The standards of precision, conciseness, and mathematical rigour which we have maintained in this text are in clearcut contrast with the majority of similar texts on the subject. The main advantage of this choice should be a considerable gain of time for the noninitiated reader, provided he or she has a taste for mathematical language. On the other hand, being fully aware of the usefulness of ARMA models for applications, we present carefully and in full detail the essential algorithms for practical modelling and identification of ARMA processes. The experience gained from several graduate courses on these themes (Universities of Paris-Sud and of Paris-7) has shown that the mathematical material included here is sufficient to build reasonable computer programs of data analysis by ARMA modelling. To facilitate the reading, we have inserted a bibliographical guide at the end of each chapter and, indicated by stars (* ... *), a few intricate mathematical points which may be skipped over by nonspecialists.

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Page Count

243

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461249120

ISBN 13

9781461249122

Homogeneous Manifolds with Negative Curvature, Part II

By: Robert Azencott,Edward N. Wilson

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Homogeneous Manifolds with Negative Curvature, Part II

By: Robert Azencott,Edward N. Wilson

This paper is the second in a series dealing with the structure of the full isometry group I(M) for M a connected, simply connected, homogeneous, Riemannian manifold with non-positive sectional curvature. It is shown that every such manifold determines canonically a conjugacy class of subgroups of I(M) which act simply transitively on M. The class of all simply transitive subgroups of I(M) is identified and it is demonstrated that an arbitrary simply transitive subgroup may be modified slightly to produce a subgroup in the canonical class. The class of all connected Lie groups G for which there exists such a manifold M with G isomorphic to the identity connected component of I(M) is identified by means of a list of structural conditions on the Lie algebra of G. Given an arbitrary connected, simply connected Riemannian manifold M together with a given simply transitive group S of isometries, an algorithm is exhibited to explicitly compute the Lie algebra of I(M) from the transported Riemannian data on S.

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Page Count

110

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821821784

ISBN 13

9780821821787

Topological Dynamics and Applications

A Volume in Honor of Robert Ellis : Proceedings of a Conference in Honor of the Retirement of Robert Ellis, April 5-6, 1995, University of Minnesota

By: Robert Ellis,Mahesh G. Nerurkar

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Topological Dynamics and Applications

A Volume in Honor of Robert Ellis : Proceedings of a Conference in Honor of the Retirement of Robert Ellis, April 5-6, 1995, University of Minnesota

By: Robert Ellis,Mahesh G. Nerurkar

This book is a very readable exposition of the modern theory of topological dynamics and presents diverse applications to such areas as ergodic theory, combinatorial number theory and differential equations. There are three parts: 1) The abstract theory of topological dynamics is discussed, including a comprehensive survey by Furstenberg and Glasner on the work and influence of R. Ellis. Presented in book form for the first time are new topics in the theory of dynamical systems, such as weak almost-periodicity, hidden eigenvalues, a natural family of factors and topological analogues of ergodic decomposition. 2) The power of abstract techniques is demonstrated by giving a very wide range of applications to areas of ergodic theory, combinatorial number theory, random walks on groups and others. 3) Applications to non-autonomous linear differential equations are shown. Exposition on recent results about Floquet theory, bifurcation theory and Lyapanov exponents is given.

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Page Count

348

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821806084

ISBN 13

9780821806081

Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

By: Robert Edward Bowen

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Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

By: Robert Edward Bowen

For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems.

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Springer

Published Date

ISBN 10

3540776958

ISBN 13

9783540776956

Group Actions in Ergodic Theory, Geometry, and Topology

Selected Papers

By: Robert J. Zimmer

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Group Actions in Ergodic Theory, Geometry, and Topology

Selected Papers

By: Robert J. Zimmer

Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.

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Page Count

724

Publisher

University of Chicago Press

Published Date

ISBN 10

022656813X

ISBN 13

9780226568133

Monte Carlo Statistical Methods

By: Christian Robert,George Casella

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Monte Carlo Statistical Methods

By: Christian Robert,George Casella

We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.

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Page Count

522

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475730713

ISBN 13

9781475730715

Schrödinger Diffusion Processes

By: Robert Aebi

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Schrödinger Diffusion Processes

By: Robert Aebi

In 1931 Erwin Schrödinger considered the following problem: A huge cloud of independent and identical particles with known dynamics is supposed to be observed at finite initial and final times. What is the "most probable" state of the cloud at intermediate times? The present book provides a general yet comprehensive discourse on Schrödinger's question. Key roles in this investigation are played by conditional diffusion processes, pairs of non-linear integral equations and interacting particles systems. The introductory first chapter gives some historical background, presents the main ideas in a rather simple discrete setting and reveals the meaning of intermediate prediction to quantum mechanics. In order to answer Schrödinger's question, the book takes three distinct approaches, dealt with in separate chapters: transformation by means of a multiplicative functional, projection by means of relative entropy, and variation of a functional associated to pairs of non-linear integral equations. The book presumes a graduate level of knowledge in mathematics or physics and represents a relevant and demanding application of today's advanced probability theory.

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Page Count

196

Publisher

Birkhäuser

Published Date

ISBN 10

3034890273

ISBN 13

9783034890274

Homogeneous Manifolds with Negative Curvature, Part II

By: Robert Azencott,Edward N. Wilson

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Homogeneous Manifolds with Negative Curvature, Part II

By: Robert Azencott,Edward N. Wilson

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Page Count

110

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American Mathematical Soc.

Published Date

ISBN 10

0821821784

ISBN 13

9780821821787

Large Deviations at Saint-Flour

By: Robert Azencott,Mark I. Freidlin,S.R.S. Varadhan

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Large Deviations at Saint-Flour

By: Robert Azencott,Mark I. Freidlin,S.R.S. Varadhan

Contents: Azencott, R. : Large deviations and applications.- Freidlin, Mark I. Semi-linear PDE's and limit theorems for large deviations- Varadhan, Srinivasa R.S.: Large deviations and applications.

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Page Count

371

Publisher

Springer

Published Date

ISBN 10

3642332013

ISBN 13

9783642332012

Series of Irregular Observations

Forecasting and Model Building

By: Robert Azencott,Didier Dacunha-Castelle

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Series of Irregular Observations

Forecasting and Model Building

By: Robert Azencott,Didier Dacunha-Castelle

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Solve jigsaw puzzle

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Page Count

243

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461249120

ISBN 13

9781461249122

Book's by Robert Azencott

Series of Irregular Observations

Series of Irregular Observations

Homogeneous Manifolds with Negative Curvature, Part II

Homogeneous Manifolds with Negative Curvature, Part II

Topological Dynamics and Applications

Topological Dynamics and Applications

Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

Group Actions in Ergodic Theory, Geometry, and Topology

Group Actions in Ergodic Theory, Geometry, and Topology

Monte Carlo Statistical Methods

Monte Carlo Statistical Methods

Schrödinger Diffusion Processes

Schrödinger Diffusion Processes

Homogeneous Manifolds with Negative Curvature, Part II

Homogeneous Manifolds with Negative Curvature, Part II

Large Deviations at Saint-Flour

Large Deviations at Saint-Flour

Series of Irregular Observations

Series of Irregular Observations

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