2 results
Ergodic behaviour of extreme values
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- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 68 / Issue 2 / April 2000
- Published online by Cambridge University Press:
- 09 April 2009, pp. 170-180
- Print publication:
- April 2000
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Let {Xn, n ≥ 1} be independent identically distributed random variables with a common non-degenerate distribution function F. For each n ≥ 1, denote Mn = max {X1,…, Xn}. Under certain conditions on F, there exist constants an > 0 and bn ∈ R such that
. In this paper, we shall show that {(Mn – bn)/an} exhibits ergodic behaviour under additional conditions of F.
. In this paper, we shall show that {(On the moments of a self-correcting process
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- Journal:
- Journal of Applied Probability / Volume 21 / Issue 2 / June 1984
- Published online by Cambridge University Press:
- 14 July 2016, pp. 335-342
- Print publication:
- June 1984
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The existence of ordinary and exponential moments of a point process with conditional intensity of the form
is deduced from a Markov chain representation for t – ρN(t). These results form an application of recent theorems of Tweedie (1983a, b) and are used to obtain laws of large numbers for a range of functionals of the process.
