Institute of Mathematical Statistics Lecture Notes - Monograph Series

Markovianity in space and time

M. N. M. van Lieshout

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Markov chains in time, such as simple random walks, are at the heart of probability. In space, due to the absence of an obvious definition of past and future, a range of definitions of Markovianity have been proposed. In this paper, after a brief review, we introduce a new concept of Markovianity that aims to combine spatial and temporal conditional independence.

Chapter information

Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy, eds., Dynamics & Stochastics: Festschrift in honor of M. S. Keane (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 154-168

First available in Project Euclid: 28 November 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 62M30: Spatial processes

Hammersley-Clifford factorisation marked point process Markov chain Monte Carlo sampling neighbour relation pairwise interaction random sequential adsorption sequential spatial process

Copyright © 2006, Institute of Mathematical Statistics


van Lieshout, M. N. M. Markovianity in space and time. Dynamics & Stochastics, 154--168, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000185.

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