Some classes of Markov processes on configuration spaces and their applications

Ohlerich N (2007)
Bielefeld (Germany): Bielefeld University.

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Bielefeld Dissertation | English
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Kondratiev, Yuri G. (Prof. Dr.)
Abstract
In dieser Arbeit werden Glauber- und Kawasaki-Dynamiken im Kontinuum studiert und einige Anwendungen von Geburts- und Sterbeprozessen auf demographische Modelle betrachtet. Eine Glauberdynamik ist ein räumlicher Geburts- und Sterbeprozess, und eine Kawasaki-Dynamik ist ein räumlicher Sprungprozess. Mithilfe der Theorie der Dirichletformen wurden equilibrium Glauber- und Kawasaki-Dynamiken mit einem Determinantal Point Process als invariantem Maß konstruiert. Es wurden auch die Spektraleigenschaften des Generators der Glauber-Dynamik untersucht und Ergebnisse für eine Klasse der Potenziale erziehlt, die zuvor nicht untersucht werden konnten.

In this work Glauber and Kawasaki dynamics for interacting particle systems in continuum are studied, and some applications of certain birth-and-death processes to demography are considered. The Glauber dynamics may be interpreted as a special birth-and-death process, whereas in the Kawasaki dynamics particles randomly jump over the space. Using the theory of Dirichlet forms we construct equilibrium Glauber and Kawasaki dynamics which have a Determinantal Point Process as an invariant measure. We also studied the spectral properties of the Glauber dynamics generator and achieved new results for a class of potentials, for which no conclusions could be gained before.
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Ohlerich N. Some classes of Markov processes on configuration spaces and their applications. Bielefeld (Germany): Bielefeld University; 2007.
Ohlerich, N. (2007). Some classes of Markov processes on configuration spaces and their applications. Bielefeld (Germany): Bielefeld University.
Ohlerich, N. (2007). Some classes of Markov processes on configuration spaces and their applications. Bielefeld (Germany): Bielefeld University.
Ohlerich, N., 2007. Some classes of Markov processes on configuration spaces and their applications, Bielefeld (Germany): Bielefeld University.
N. Ohlerich, Some classes of Markov processes on configuration spaces and their applications, Bielefeld (Germany): Bielefeld University, 2007.
Ohlerich, N.: Some classes of Markov processes on configuration spaces and their applications. Bielefeld University, Bielefeld (Germany) (2007).
Ohlerich, Nataliya. Some classes of Markov processes on configuration spaces and their applications. Bielefeld (Germany): Bielefeld University, 2007.
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