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Asymptotic distributions of pontograms

Published online by Cambridge University Press:  24 October 2008

Miklós Csörgő  and
Lajos Horváth
Miklós Csörgő
Affiliation:
Department of Mathematics and Statistics, Carleton University
Lajos Horváth
Affiliation:
Bolyai Institute, Szeged University
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Extract

Let{N(x), x ≥ 0} be a Poisson process with intensity parameter λ > 0, and introduce

When looking for the changepoint in the Land's End data, Kendall and Kendall [7] proved for all 0 < ε1 < 1 − ε2 < 1 that

where {V(s), − ∞ < s < ∞} is an Ornstein–Uhlenbeck process with covariance function exp (−|t − s|). D. G. Kendall has posed the problem of replacing ε1 and ε2 by zero or by sequences εi(n) → 0 (n → ∞) (i = 1, 2), in (1·1). In this paper we study the latter problem and also its L2 version. The proofs will be based on the following weighted approximation of Zn.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 1 , January 1987 , pp. 131 - 139
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

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