Large deviations for some weakly dependent random processes. (English) Zbl 0699.60016

The authors prove large deviation principles for two classes of weakly dependent processes, moving averages of i.i.d. random variables and Poisson center cluster random measures. After publication the authors have been informed that the result for moving averages is known [see J. Steinebach, Asymptotic Statistics 2, Proc. 3rd Prague Symp. 1983, Asymptotic Stat. 2, 405-415 (1984; Zbl 0568.60034), and K. Singh, J. Multivariate Anal. 11, 354-367 (1981; Zbl 0464.60027)].
Reviewer: H.Dehling


60F10 Large deviations
Full Text: DOI


[1] Burton, R.M.; Waymire, E., Scaling limits for associated random measures, Ann. probab., 4, 1267-1278, (1985) · Zbl 0579.60039
[2] Denker, M., Large deviations and the pressure function, (1988), Preprint
[3] Ellis, R.S., Entropy, large deviations and statistical mechanics, (1985), Springer New York · Zbl 0566.60097
[4] Kallenberg, O., ()
[5] Lebowitz, J.L.; Schonmann, R.H., Pseudo-free energies and large deviations for non-Gibbsian FKG measures, Probab. theory rel. fields, 77, 49-64, (1988) · Zbl 0617.60097
[6] Matthes, K.; Kerstan, J.; Mecke, J., Infinitely divisible point processes, (1978), Wiley New York · Zbl 0521.60056
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