Quasi-stationary distributions Markov chains, diffusions and dynamical systems by Pierre Collet, Servet Martínez, Jaime San Martín

Format:

Book

Author/Creator:

Collet, Pierre, 1948-

Contributor:

Martínez, Servet

San Martín, Jaime

Series:

Probability and its applications 1431-7028

Language:

English

Subjects (All):

Distribution (Probability theory).

Markov processes.

Markov Chains.

distribution (statistics-related concept).

Medical Subjects:

Markov Chains.

Physical Description:

1 online resource

Place of Publication:

Berlin Heidelberg Springer 2013

Language Note:

English

System Details:

text file

PDF

Summary:

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

Contents:

Introduction

Quasi-stationary distributions : general results

Markov chains on finite spaces

Markov chains on countable spaces

Birth and death chains

Regular diffusions on [0,∞)

Infinity as entrance boundary

Dynamical systems

Notes:

Includes bibliographical references (pages 269-273), index, table of notations, and citations index

Other Format:

Print version Collet, Pierre, 1948- Quasi-stationary distributions

ISBN:

9783642331312

3642331319

3642331300

9783642331305

1283909898

9781283909891

OCLC:

820818723

Access Restriction:

Restricted for use by site license