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Remarks on a Markov chain example of Kolmogorov

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1969
It is shown that the stochastic transition matrix P(t), in Kolmogorov's example of a process with an instantaneous state, is uniquely determined by the derivative matrix Q=P′(0), and the most general such substochastic P(t) is also found. The example is used to show that, if 0 is an instantaneous state, then 1-p 00(t) can tend to 0 arbitrarily slowly ...
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Examples of Analyses Based on Continuous Time Markov Chain Modelling

1992
Abstract In this chapter we give some examples of practical applications of analyses based on CTMCs and their generalizations. The examples are partially based on our collaborative projects with experimental research groups (i.e.
Patsy Haccou, Evert Meelis
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An example on geometric ergodicity of a finite Markov chain

Journal of Applied Probability, 1972
A discrete time Markov chain with (n + 1) states is constructed in which there are n states having different decay parameters for geometric ergodicity.
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Examples of Continuous-Time Markov Chains

1991
In this case we have a finite state space E which we can take to be \(\left\{ {1,2,3,...,n} \right\}\). Given any q-matrix Q, which need not be conservative, there is a unique Q-function, and we can solve either the backward or forward equations to find it.
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An example of complex modelling in dentistry using Markov chain Monte Carlo (MCMC) simulation.

Community dental health, 2002
In the usual regression setting one regression line is computed for a whole data set. In a more complex situation, each person may be observed for example at several points in time and thus a regression line might be calculated for each person.
Helfenstein, Ulrich   +3 more
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Markov chain approach to analyze the dynamics of pathogen fecal shedding—Example of Listeria monocytogenes shedding in a herd of dairy cattle

Journal of Theoretical Biology, 2007
Fecal shedding is an important mechanism of spreading of a number of human and animal pathogens. Understanding of the dynamics of pathogen fecal shedding is critical to be able to control or prevent the spread of diseases caused by these pathogens.
Ivanek, Renata   +3 more
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Assessing the convergence of Markov Chain Monte Carlo methods: An example from evaluation of diagnostic tests in absence of a gold standard

Preventive Veterinary Medicine, 2007
The accessibility of Markov Chain Monte Carlo (MCMC) methods for statistical inference have improved with the advent of general purpose software. This enables researchers with limited statistical skills to perform Bayesian analysis. Using MCMC sampling to do statistical inference requires convergence of the MCMC chain to its stationary distribution ...
Toft, N.   +3 more
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Application of Markov chain and entropy analysis to lithologic successions: An example from the Cretaceous of the Benue trough (Nigeria)

Geologische Rundschau, 1985
Eine Markov'sche Kettenanalyse wird in der Untersuchung von zwei stratigraphischen Ausschnitten aus der Kreide des Benue-Troges in Nigeria eingesetzt. Vier Faziesabschnitte bestehend aus grobkornigem, mittelkornigem und feinem Sandstein sowie Tonstein, lassen sich trennen.
Hoque, M., Nwajide, C. S.
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Fitting feature-dependent Markov chains

Journal of Global Optimization, 2022
Shane T. Barratt, S. Boyd
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Bounding convergence rates for Markov chains: An example of the use of computer algebra

Statistics and Computing, 2001
Kolassa and Tanner (J. Am. Stat. Assoc. (1994) 89, 697–702) present the Gibbs-Skovgaard algorithm for approximate conditional inference. Kolassa (Ann Statist. (1999), 27, 129–142) gives conditions under which their Markov chain is known to converge.
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