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Quasi-Stationary Distributions: Markov Chains, Diffusions and Dynamical Systems (Probability and Its Applications)

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Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This book explores the main concepts of quasi-stationary distributions (QSDs) for killed processes. The authors offer numerous examples, and provide a basis for applications in mathematical ecology, statistical physics, computer sciences and economics.

Table of Contents

1.Introduction.- 2.Quasi-stationary Distributions: General Results.- 3.Markov Chains on Finite Spaces.- 4.Markov Chains on Countable Spaces.- 5.Birth and Death Chains.- 6.Regular Diffusions on [0,∞).- 7.Infinity as Entrance Boundary.- 8.Dynamical Systems.- References.- Index.- Table of Notations.- Citations Index.

Product Details

ISBN:
9783642331305
Author:
Collet, Pierre
Publisher:
Springer
Author:
San Martin, Jaime
Author:
Jaime San Martin
Author:
Martinez, Servet
Location:
Berlin, Heidelberg
Subject:
Mathematics-Applied
Subject:
Statistics
Subject:
60J70, 60JXX, 60J10, 60J60, 60J65, 92Dxx, 37DXX, 35PXX
Subject:
Markov Chains
Subject:
absorption problems
Subject:
Diffusion processes.
Subject:
hyperbolic dynamical systems
Subject:
Population dynamics.
Subject:
Probability Theory and Stochastic Processes
Subject:
Dynamical Systems and Ergodic Theory
Subject:
Genetics and Population Dynamics
Subject:
PARTIAL DIFFERENTIAL EQUATIONS
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Distribution (Probability theory)
Subject:
Differentiable dynamical systems
Subject:
Genetics_xMathematics
Subject:
Differential equations, partial
Copyright:
Edition Description:
2013
Series:
Probability and Its Applications
Publication Date:
20121127
Binding:
HARDCOVER
Language:
English
Pages:
350
Dimensions:
235 x 155 mm

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Related Subjects


Science and Mathematics » Biology » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Probability Theory
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Quasi-Stationary Distributions: Markov Chains, Diffusions and Dynamical Systems (Probability and Its Applications) New Hardcover
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Product details 350 pages Springer - English 9783642331305 Reviews:
"Synopsis" by , This book explores the main concepts of quasi-stationary distributions (QSDs) for killed processes. The authors offer numerous examples, and provide a basis for applications in mathematical ecology, statistical physics, computer sciences and economics.
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