Author: Pierre Collet
Publisher: Springer Science & Business Media
ISBN: 3642331300
Category : Mathematics
Languages : en
Pages : 288
Get Book Here
Book Description
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.
Author: Pierre Collet
Publisher: Springer Science & Business Media
ISBN: 3642331319
Category : Mathematics
Languages : en
Pages : 288
Get Book Here
Book Description
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.
Author: Pierre Collet
Publisher: Springer
ISBN: 9783642428883
Category : Mathematics
Languages : en
Pages : 0
Get Book Here
Book Description
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.
Author: Barry Richard Flannery
Publisher:
ISBN:
Category :
Languages : en
Pages : 206
Get Book Here
Book Description
Author: Leonidas Zitis
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: Naoki Makimoto
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
Get Book Here
Book Description
Author: STANFORD UNIV CA DEPT OF STATISTICS.
Publisher:
ISBN:
Category :
Languages : en
Pages : 8
Get Book Here
Book Description
It is shown that if a stochastically monotone Markov process of (0, infinity) with stationary distribution H has its state space truncated by making all states in (B, infinity) absorbing, then the quasi-stationary distribution of the new process coverages to H as B approaches limit of infinity. (Author).
Author: Ingemar Nåsell
Publisher: Springer Science & Business Media
ISBN: 3642205291
Category : Mathematics
Languages : en
Pages : 206
Get Book Here
Book Description
This volume presents explicit approximations of the quasi-stationary distribution and of the expected time to extinction from the state one and from quasi-stationarity for the stochastic logistic SIS model. The approximations are derived separately in three different parameter regions, and then combined into a uniform approximation across all three regions. Subsequently, the results are used to derive thresholds as functions of the population size N.
Author: David C. Flaspohler
Publisher:
ISBN:
Category :
Languages : en
Pages : 10
Get Book Here
Book Description
The stationary conditional doubly limiting conditional and limiting conditional mean ratio quasi-stationary distributions are given for continuous time Markov Chains with denumerable state space. (Author).
Author: Naoki Makimoto
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
Get Book Here
Book Description
