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＜電子ブック＞
Quasi-Stationary Distributions : Markov Chains, Diffusions and Dynamical Systems / by Pierre Collet, Servet Martínez, Jaime San Martín
(Probability and Its Applications)

版	1st ed. 2013.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2013
本文言語	英語
大きさ	XVI, 280 p : online resource
著者標目	*Collet, Pierre author Martínez, Servet author San Martín, Jaime author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Dynamical systems LCSH:Population genetics LCSH:Differential equations FREE:Probability Theory FREE:Dynamical Systems FREE:Population Genetics FREE:Differential Equations
一般注記	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.  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 findingsdescribed 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 HTTP:URL=https://doi.org/10.1007/978-3-642-33131-2

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