Extreme Value Theory for a Class of Markov Chains with Values in ℝd
1997 ◽
Vol 29
(01)
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pp. 138-164
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Keyword(s):
We consider extreme value theory for a class of stationary Markov chains with values in ℝd. The asymptotic distribution of M n , the vector of componentwise maxima, is determined under mild dependence restrictions and suitable assumptions on the marginal distribution and the transition probabilities of the chain. This is achieved through computation of a multivariate extremal index of the sequence, extending results of Smith [26] and Perfekt [21] to a multivariate setting. As a by-product, we obtain results on extremes of higher-order, real-valued Markov chains. The results are applied to a frequently studied random difference equation.
2016 ◽
Vol 16
(03)
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pp. 1660015
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1986 ◽
Vol 23
(04)
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pp. 937-950
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Keyword(s):
1986 ◽
Vol 23
(04)
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pp. 937-950
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Keyword(s):
Keyword(s):
2004 ◽
Vol 2004
(3)
◽
pp. 211-228
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1985 ◽
2006 ◽
Vol 1
(2)
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pp. 51-57
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Keyword(s):