Extremal processes and record value times
- 1 December 1973
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 10 (4) , 864-868
- https://doi.org/10.2307/3212388
Abstract
Let {Xn, n ≧ 1} be i.i.d. and Yn = max {X1,…, Xn}. Xj is a record value of {Xn} if Yj > Yj–1 The record value times are Ln, n ≧ 1 and inter-record times are Δn, n ≧ 1. The known limiting behavior of {Ln} and {Δn} is close to that of a non-homogeneous Poisson process and an explanation of this is obtained by embedding {Yn} in a suitable extremal process which jumps according to a non-homogeneous Poisson process.Keywords
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