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Stochastic Population ProcessesAnalysis, Approximations, Simulations$
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Eric Renshaw

Print publication date: 2011

Print ISBN-13: 9780199575312

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199575312.001.0001

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Spatial–temporal extensions

Spatial–temporal extensions

Chapter:
(p.575) 10 Spatial–temporal extensions
Source:
Stochastic Population Processes
Author(s):

Eric Renshaw

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199575312.003.0010

Although the Turing model and the Markov chain process are both ideal for studying systems which involve spatial interaction between adjacent sites, in practice interaction may occur across much larger spatial levels. Moreover, there is no reason why locations have to lie on a lattice structure, which has been our presumption so far in order to enable some degree of mathematical tractability. This chapter presents two extensions to earlier spatial analyses. The first introduces the concept of long-range dependence, whilst the second examines processes which develop over real, rather than discrete, space.

Keywords:   spatial analyses, long-range dependence, real space, Turing model, Markov chain processes

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