Poisson and extreme value limit theorems for Markov random fields
1987 ◽
Vol 19
(01)
◽
pp. 106-122
◽
Keyword(s):
Let Xt , be a Markov random field assuming values in RM. Let In be a rectangular box in Zm with its center at 0 and corner points with coordinates ±n. Let (An ) be a sequence of measurable subsets of RM such that neighborhood of t) → 0, for n → ∞; and let fn (x) be the indicator of An. Under appropriate conditions on the nearest-neighbor distributions of (Xt ), the conditional distribution of given the values of Xs , for s on the boundary of In , converges to the Poisson distribution. An immediate application is an extreme value limit theorem for a real-valued Markov random field.
1992 ◽
Vol 29
(04)
◽
pp. 877-884
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1996 ◽
Vol 28
(01)
◽
pp. 1-12
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Keyword(s):
Keyword(s):