Markovianity in space and time

Mathematics – Probability

Scientific paper

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Published at http://dx.doi.org/10.1214/074921706000000185 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

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.

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