Displaying similar documents to “A quenched weak invariance principle”

Why the Kemeny Time is a constant

Karl Gustafson, Jeffrey J. Hunter (2016)

Special Matrices

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We present a new fundamental intuition forwhy the Kemeny feature of a Markov chain is a constant. This new perspective has interesting further implications.

On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains

Ion Grama, Émile Le Page, Marc Peigné (2014)

Colloquium Mathematicae

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We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is controlled by an assumption on the characteristic function of the finite-dimensional increments of the process. The distinctive feature of the new mixing condition is that the dependence increases exponentially in the dimension of the increments. The proposed...

Reduction of absorbing Markov chain

Mariusz Górajski (2009)

Annales UMCS, Mathematica

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In this paper we consider an absorbing Markov chain with finite number of states. We focus especially on random walk on transient states. We present a graph reduction method and prove its validity. Using this method we build algorithms which allow us to determine the distribution of time to absorption, in particular we compute its moments and the probability of absorption. The main idea used in the proofs consists in observing a nondecreasing sequence of stopping times. Random walk on...

Central limit theorem for hitting times of functionals of Markov jump processes

Christian Paroissin, Bernard Ycart (2010)

ESAIM: Probability and Statistics

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A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.

On the exchanges between Wolfgang Doeblin and Bohuslav Hostinský

Laurent Mazliak (2007)

Revue d'histoire des mathématiques

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We present the letters sent by Wolfgang Doeblin to Bohuslav Hostinský between 1936 and 1938. They concern some aspects of the general theory of Markov chains and the solutions of the Chapman-Kolmogorov equation that Doeblin was then establishing for his PhD thesis.