Institute of Mathematical Statistics Lecture Notes - Monograph Series

Markovianity in space and time

M. N. M. van Lieshout

Full-text: Open access

Abstract

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

Source
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

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196285817

Digital Object Identifier
doi:10.1214/074921706000000185

Mathematical Reviews number (MathSciNet)
MR2306197

Zentralblatt MATH identifier
1131.60044

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

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

Citation

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. https://projecteuclid.org/euclid.lnms/1196285817


Export citation