Asymptotic distributions of weighted compound Poisson bridges
Published online by Cambridge University Press: 24 October 2008
Extract
Let S(N(t)) be defined by
where {N(t), t ≥ 0} is a Poisson process with intensity parameter 1/μ > 0 and {Xi i ≥ 1} is a family of independent random variables which are also independent of {N(t), t ≥ 0}.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 3 , November 1992 , pp. 613 - 629
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- Copyright © Cambridge Philosophical Society 1992
References
REFERENCES
[2]Chibisov, D.. Some theorems on the limiting behaviour of empirical distribution functions. Selected Transl. Math. Statist. Probab. 6 (1964), 147–156.Google Scholar
[4]Csörgő, M., Csörgő, S. and Horváth, L.. An Asymptotic Theory for Empirical Reliability and Concentration Processes. Lecture Notes in Statist, vol. 33 (Springer-Verlag 1986).CrossRefGoogle Scholar
[5]Csörgő, M., Csörgő, S., Horváth, L. and Mason, D.. Weighted empirical and quantile processes. Ann. Probab. 14 (1986), 31–85.CrossRefGoogle Scholar
[6]Csörgő, M., Deheuvels, P. and Horváth, L.. An approximation of stopped sums with applications in queueing theory. Adv. in Appl. Probab. 19 (1987), 674–690.CrossRefGoogle Scholar
[7]Csörgő, M. and Horváth, L.. Asymptotic distributions of pontograms. Math. Proc. Cambridge Philos. Soc. 101 (1987), 131–139.CrossRefGoogle Scholar
[8]Csörgő, M. and Horváth, L.. On the distributions of L p norms of weighted uniform empirical and quantile processes. Ann. Probab. 16 (1988), 142–161.CrossRefGoogle Scholar
[9]Csörgő, M. and Horváth, L.. Weighted Approximations in Probability and Statistics, book in preparation.Google Scholar
[10]Csörgő, M., Horváth, L. and Shao, Q. M.. Random integrals and summability of partial sums. Stochastic Process. Appl., to appear.Google Scholar
[11]Csörgő, M. and Révész, P.. Strong Approximations in Probability and Statistics (Academic Press 1981).Google Scholar
[12]Csörgő, M., Shao, Q. M. and Szyszkowicz, B.. A note on local and global functions of a Wiener process and some Rényi-type statistics. Studia Sci. Math. Hungar. 26 (1991), in press.Google Scholar
[13]Darling, D. A. and Erdős, P.. A limit theorem for the maximum of normalized sums of independent random variables. Duke Math. J. 23 (1956), 143–145.CrossRefGoogle Scholar
[14]Eastwood, V. R.. Some recent developments concerning asymptotic distributions of pontograms. Math. Proc. Cambridge Philos. Soc. 108 (1990), 559–567.CrossRefGoogle Scholar
[15]Greenwood, P. E. and Shiryayev, A. N.. Contiguity and the Statistical Invariance Principle (Gordon and Breach, 1985).Google Scholar
[17]Ito, K. and MoKean, H. P. Jr. Diffusion Processes and their Sample Paths (Springer-Verlag 1965).Google Scholar
[18]Kendall, D. G. and Kendall, W. S.. Alignments in two-dimensional random sets of points. Adv. in Appl. Probab. 12 (1980), 380–424.CrossRefGoogle Scholar
[19]Khmaladze, E. V. and Parjanadze, A. M.. Functional limit theorems for linear statistics of sequential ranks. Probab. Theory Related Fields 73 (1986), 322–334.CrossRefGoogle Scholar
[20]Le Cam, L.. Locally asymptotically normal families of distributions. Univ. California Publ. Statist.. 3 (1960), 37–98.Google Scholar
[21]Le Cam, L.. Asymptotic Methods in Statistical Decision Theory (Springer-Verlag, 1986).CrossRefGoogle Scholar
[22]O'Reilly, N.. On the weak convergence of empirical processes in sup-norm metrics. Ann. Probab. 2 (1974), 642–651.CrossRefGoogle Scholar
[23]Roussas, G. G.. Contiguity of Probability Measures: Some Applications in Statistics (Cambridge University Press 1972).CrossRefGoogle Scholar
[24]Szyszkowicz, B.. Changepoint problem and contiguous alternatives. Statist. Probab. Lett. 11 (1991), 299–308.CrossRefGoogle Scholar
[25]Szyszkowicz, B.. Asymptotic distributions of weighted pontograms under contiguous alternatives. Math. Proc. Cambridge Philos. Soc. 112 (1992), 431–447.CrossRefGoogle Scholar
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