Open Access
VOL. 48 | 2006 Markovianity in space and time
M. N. M. van Lieshout

Editor(s) Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy

IMS Lecture Notes Monogr. Ser., 2006: 154-168 (2006) DOI: 10.1214/074921706000000185


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.


Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1131.60044
MathSciNet: MR2306197

Digital Object Identifier: 10.1214/074921706000000185

Primary: 60D05 , 60G55
Secondary: 62M30

Keywords: Hammersley-Clifford factorisation , marked point process , Markov chain , Monte Carlo sampling , neighbour relation , pairwise interaction , Random sequential adsorption , sequential spatial process

Rights: Copyright © 2006, Institute of Mathematical Statistics

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