000 03815nam a22005535i 4500
001 978-3-642-33131-2
003 DE-He213
005 20140220082854.0
007 cr nn 008mamaa
008 121026s2013 gw | s |||| 0|eng d
020 _a9783642331312
_9978-3-642-33131-2
024 7 _a10.1007/978-3-642-33131-2
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aCollet, Pierre.
_eauthor.
245 1 0 _aQuasi-Stationary Distributions
_h[electronic resource] :
_bMarkov Chains, Diffusions and Dynamical Systems /
_cby Pierre Collet, Servet Martínez, Jaime San Martín.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXV, 280 p. 15 illus., 12 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProbability and Its Applications,
_x1431-7028
505 0 _a1.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. .
520 _aMain 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.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aDifferential equations, partial.
650 0 _aGenetics
_xMathematics.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aGenetics and Population Dynamics.
650 2 4 _aPartial Differential Equations.
700 1 _aMartínez, Servet.
_eauthor.
700 1 _aSan Martín, Jaime.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642331305
830 0 _aProbability and Its Applications,
_x1431-7028
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-33131-2
912 _aZDB-2-SMA
999 _c97337
_d97337