Servet Martinez's Books

Neural and Automata Networks

Dynamical Behavior and Applications

By: E. Goles,Servet Martínez

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Neural and Automata Networks

Dynamical Behavior and Applications

By: E. Goles,Servet Martínez

Et moi ..., si j'avait Sll comment en revenir. One sennce mathematics has rendered the human race. It has put common sense back je n'y serais point alle.' Jules Verne whe", it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be smse'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'!ltre of this series

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259

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Springer Science & Business Media

Published Date

ISBN 10

9400905297

ISBN 13

9789400905290

Quasi-Stationary Distributions

Markov Chains, Diffusions and Dynamical Systems

By: Pierre Collet,Servet Martínez,Jaime San Martín

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Quasi-Stationary Distributions

Markov Chains, Diffusions and Dynamical Systems

By: Pierre Collet,Servet Martínez,Jaime San Martín

Main concepts of quasi-stationary distributions (QSDs) for killed processes are the focus of the present volume. For diffusions, the killing is at the boundary and for dynamical systems there is a trap. The authors present the QSDs as the ones that allow describing the long-term behavior conditioned to not being killed. Studies in this research area started with Kolmogorov and Yaglom and in the last few decades have received a great deal of attention. The authors provide the exponential distribution property of the killing time for QSDs, present the more general result on their existence and study the process of trajectories that survive forever. For birth-and-death chains and diffusions, the existence of a single or a continuum of QSDs is described. They study the convergence to the extremal QSD and give the classification of the survival process. In this monograph, the authors discuss Gibbs QSDs for symbolic systems and absolutely continuous QSDs for repellers. The findings described are relevant to researchers in the fields of Markov chains, diffusions, potential theory, dynamical systems, and in areas where extinction is a central concept. The theory is illustrated with numerous examples. The volume uniquely presents the distribution behavior of individuals who survive in a decaying population for a very long time. It also provides the background for applications in mathematical ecology, statistical physics, computer sciences, and economics.

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288

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Springer Science & Business Media

Published Date

ISBN 10

3642331300

ISBN 13

9783642331305

Inverse M-Matrices and Ultrametric Matrices

By: Claude Dellacherie,Servet Martinez,Jaime San Martin

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Inverse M-Matrices and Ultrametric Matrices

By: Claude Dellacherie,Servet Martinez,Jaime San Martin

The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains. The main focus of this monograph is the so-called inverse M-matrix problem, which asks for a characterization of nonnegative matrices whose inverses are M-matrices. We present an answer in terms of discrete potential theory based on the Choquet-Deny Theorem. A distinguished subclass of inverse M-matrices is ultrametric matrices, which are important in applications such as taxonomy. Ultrametricity is revealed to be a relevant concept in linear algebra and discrete potential theory because of its relation with trees in graph theory and mean expected value matrices in probability theory. Remarkable properties of Hadamard functions and products for the class of inverse M-matrices are developed and probabilistic insights are provided throughout the monograph.

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241

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Springer

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ISBN 10

3319102982

ISBN 13

9783319102986

Quasi-Stationary Distributions

Markov Chains, Diffusions and Dynamical Systems

By: Pierre Collet,Servet Martínez,Jaime San Martín

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Quasi-Stationary Distributions

Markov Chains, Diffusions and Dynamical Systems

By: Pierre Collet,Servet Martínez,Jaime San Martín

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Solve jigsaw puzzle

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Page Count

288

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642331300

ISBN 13

9783642331305

Neural and Automata Networks

Dynamical Behavior and Applications

By: E. Goles,Servet Martínez

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Neural and Automata Networks

Dynamical Behavior and Applications

By: E. Goles,Servet Martínez

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

259

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9400905297

ISBN 13

9789400905290

Book's by Servet Martinez

Neural and Automata Networks

Neural and Automata Networks

Quasi-Stationary Distributions

Quasi-Stationary Distributions

Inverse M-Matrices and Ultrametric Matrices

Inverse M-Matrices and Ultrametric Matrices

Quasi-Stationary Distributions

Quasi-Stationary Distributions

Neural and Automata Networks

Neural and Automata Networks

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