Extremal processes and record value times
- 1 March 1973
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 10 (04) , 864-868
- https://doi.org/10.1017/s0021900200096054
Abstract
Let {Xn , n ≧ 1} be i.i.d. and Yn = max {X 1,…, 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 Δ n , 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
This publication has 8 references indexed in Scilit:
- The structure of extremal processesAdvances in Applied Probability, 1973
- On record values and record timesJournal of Applied Probability, 1972
- A limit theorem for inter-record timesJournal of Applied Probability, 1972
- The two-dimensional Poisson process and extremal processesJournal of Applied Probability, 1971
- On the law of the iterated logarithm for inter-record timesJournal of Applied Probability, 1970
- A note on the waiting times between record observationsJournal of Applied Probability, 1969
- On outstanding values in a sequence of random variablesProbability Theory and Related Fields, 1969
- Waitingtimes between record observationsJournal of Applied Probability, 1967