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Catalogue Information
Field name	Details
Dewey Class	519.2
Title	Quasi-Stationary Distributions ([Ebook]) : Markov Chains, Diffusions and Dynamical Systems / by by Pierre Collet, Servet Martínez, Jaime San Martín
Author	Collet, Pierre. , 1948-
Added Personal Name	Martínez, Servet
Added Personal Name	San Martín, Jaime
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer
Publication	, 2013.
Physical Details	XV, 280 pages: 15 illus., 12 illus. in color. : online resource.
Series	Probability and Its Applications 1431-7028
ISBN	9783642331312
Summary Note	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 note	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,â) -- 7.Infinity as Entrance Boundary -- 8.Dynamical Systems -- References -- Index -- Table of Notations -- Citations Index.
System details note	Online access to this digital book is restricted to subscription institutions and through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-642-33131-2
Links to Related Works	Subject References: Differentiable dynamical systems . Differential equations, Partial . Distribution (Probability theory) . Dynamical systems and ergodic theory . Genetics and Population Dynamics . Mathematics . Partial differential equations . Probability theory and stochastic processes . Authors: author . Collet, Pierre. 1948- . Martínez, Servet . San Martín, Jaime . Corporate Authors: SpringerLink (Online service) . Series: Probability and Its Applications . Classification: 519.2 . 519.2 (DDC 22) .

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Quasi-Stationary Distributions: Markov Chains, Diffusions and Dynamical Systems

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