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Author: Richard Durrett Publisher: ISBN: Category : Limit theorems (Probability theory) Languages : en Pages : 158
Book Description
Let U sub k be a discrete time Markov process with state space E and let S be a proper subset of E. In several applications it is of interest to know the behavior of the system after a large number of steps given that the process has not entered S. for example if U sub k is a branching process a limit theorem of this type gives information about the size of the kth generation given that extinction has not occurred by time k.
Author: Richard Durrett Publisher: ISBN: Category : Limit theorems (Probability theory) Languages : en Pages : 158
Book Description
Let U sub k be a discrete time Markov process with state space E and let S be a proper subset of E. In several applications it is of interest to know the behavior of the system after a large number of steps given that the process has not entered S. for example if U sub k is a branching process a limit theorem of this type gives information about the size of the kth generation given that extinction has not occurred by time k.
Author: Dmitrii S. Silvestrov Publisher: Springer Science & Business Media ISBN: 0857293907 Category : Mathematics Languages : en Pages : 408
Book Description
This volume is the first to present a state-of-the-art overview of this field, with many results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast and technically demanding Russian literature in detail. Its coverage is thorough, streamlined and arranged according to difficulty.
Author: Hubert Hennion Publisher: Springer ISBN: 3540446230 Category : Mathematics Languages : en Pages : 150
Book Description
The usefulness of from the of techniques perturbation theory operators, to kernel for limit theorems for a applied quasi-compact positive Q, obtaining Markov chains for stochastic of or dynamical by describing properties systems, of Perron- Frobenius has been demonstrated in several All use a operator, papers. these works share the features the features that must be same specific general ; used in each stem from the nature of the functional particular case precise space where the of is and from the number of quasi-compactness Q proved eigenvalues of of modulus 1. We here a functional framework for Q give general analytical this method and we the aforementioned behaviour within it. It asymptotic prove is worth that this framework is to allow the unified noticing sufficiently general treatment of all the cases considered in the literature the previously specific ; characters of model translate into the verification of of simple hypotheses every a functional nature. When to Markov kernels or to Perr- applied Lipschitz Frobenius associated with these statements rise operators expanding give maps, to new results and the of known The main clarify proofs already properties. of the deals with a Markov kernel for which 1 is a part quasi-compact Q paper of modulus 1. An essential but is not the simple eigenvalue unique eigenvalue element of the work is the of the of peripheral Q precise description spectrums and of its To conclude the the results obtained perturbations.
Author: Götz Kersting Publisher: John Wiley & Sons ISBN: 1119473551 Category : Mathematics Languages : en Pages : 311
Book Description
Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.
Author: Richard Durrett
Author: Richard Durrett
Author: Reinhard Höpfner
Author: Reinhard Höpfner
Author: Dmitrii S. Silvestrov
Author: Reinhard Höpfner
Author: Burton Herbert Singer
Author: Sidney C. Port
Author: Hubert Hennion
Author: Boris Nahapetian
Author: Götz Kersting