Limit theorems for bivariate Appell polynomials. Part I: Central limit theorems

Probability Theory and Related Fields

Volumn 107, Issue 3, 1997, Pages 359-381

  Giraitis, Liudas ^a   Taqqu, Murad S ^a  

^a Boston University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031487197     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050089     Document Type: Article

References (26)

1. Avram, F.: On bilinear forms in Gaussian random variables and Toeplitz matrices. Probab. Theory Relat. Fields 79(1) 37-46 (1988)
2. Avram, F., Taqqu, M. S.: Noncentral limit theorems and Appell polynomials. Ann. Probab. 15, 767-775 (1987)
3. Billingsley, P.: Probability and Measure, 2nd edn. Wiley, New York 1986
4. Breuer, P., Major, P.: Central limit theorems for non-linear functionals of Gaussian fields. J. Multivariate Analysis 13, 425-441 (1983)
5. Dahlhaus, R.: Efficient parameter estimation for self similar processes. Ann. Statistics 17(4) 1749-1766 (1989)
6. Dobrushin, R. L., Major, P.: Non-central limit theorems for non-linear functions of Gaussian fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete 50, 27-52 (1979)
7. Fox, R., Taqqu, M. S.: Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statistics 14, 517-532 (1986)
8. Fox, R., Taqqu, M. S.: Central limit theorems for quadratic forms in random variables having long-range dependence. Probab. Theory Relat. Fields 74, 213-240 (1987)
9. Giraitis, L., Surgailis, D.: Multivariate Appell polynomials and the central limit theorem. In: Eberlein, E., Taqqu, M.S. (eds.) Dependence in Probability and Statistics. Birkhäuser, New York 1986
10. Giraitis, L., Surgailis, D.: A central limit theorem for quadratic forms in strongly dependent linear variables and application to asymptotical normality of Whittle's estimate. Probab. Theory Relat. Fields 86, 87-104 (1990)
11. Giraitis, L., Taqqu, M. S.: Central limit theorems for quadratic forms with time-domain conditions. Preprint. (1996)
12. Ho, H. C., Hsing, T.: On the asymptotic expansion of the empirical process of long memory moving averages Preprint (1995)
13. Ho, H. C., Sun, T. C.: A central limit theorem for non-instantaneous filters of a stationary Gaussian process. J. Multivariate Analysis 22, 144-155 (1987)
14. Ibragimov, I. A., Linnik, Y. V.: Independent and stationary sequences of random variables. Wolters-Nordhoff, The Netherlands 1971
15. Klüppelberg, C., Mikosch, T.: Gaussian limit fields for the integrated periodogram. Preprint (1995)
16. Kluppelberg, C., Mikosch, T.: Self-normalized and randomly centered spectral estimates. In: Proceedings of the Athens Conference on Applied Probability and Time Series Analysis. Springer-Verlag, New York. Time series volume in honour of E. J. Hannan. To appear (1996)
17. Leland, W. E., Taqqu, M. S., Willinger, W., Wilson, D. V.: On the self-similar nature of Ethernet traffic. Comput. Commun. Rev. 23, 183-193 (1993). Proceedings of the ACM/SIGCOMM'93, San Francisco, September 1993. Reprinted in: Trends in Networking - Internet, the conference book of the Spring 1995 Conference of the National Unix User Group of the Netherlands (NLUUG). Also reprinted in: Comput. Commun. Rev. 25, Nb. 1, 202-212 (1995), a special anniversary issue devoted to "Highlights from 25 years of the Computer Communications Review".
18. Leland, W. E., Taqqu, M. S., Willinger, W., Wilson, D. V.: On the self-similar nature of Ethernet traffic. Comput. Commun. Rev. 23, 183-193 (1993). Proceedings of the ACM/SIGCOMM'93, San Francisco, September 1993. Reprinted in: Trends in Networking - Internet, the conference book of the Spring 1995 Conference of the National Unix User Group of the Netherlands (NLUUG). Also reprinted in: Comput. Commun. Rev. 25, Nb. 1, 202-212 (1995), a special anniversary issue devoted to "Highlights from 25 years of the Computer Communications Review".
19. Leland, W. E., Taqqu, M. S., Willinger, W., Wilson, D. V.: On the Self-similar nature of Ethernet traffic (Extended version). IEEE/ACM Trans. Networking 2, 1-15 (1994)
20. Robinson, P. M.: Serniparametric analysis of long-memory time series. Ann. Statistics 22, 515-539 (1994a)
21. Robinson, P. M. Time series with strong dependence. In: Advances in Econometrics. Sixth World Congress., Cambridge University Press, vol. 1, Chap. 2, pp. 47-95 (1994b)
22. Robinson, P. M.: Gaussian semiparametric estimation of long range dependence. Ann. Statistics 23, 1630-1661 (1995)
23. Taqqu, M. S.: Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrscheinlichkeitstheorie verw. Gebiete 31, 287-302 (1975)
24. Terrin, N., Taqqu, M. S.: A noncentral limit theorem for quadratic forms of Gaussian stationary sequences. J. Theor. Probab. 3, 449-475 (1990)
25. Terrin, N., Taqqu, M. S.: Convergence in distribution of sums of bivariate Appell polynomials with long-range dependence. Probab. Theory Relat. Fields 90, 57-81 (1991)
26. Zygmund, A.: Trigonometric Series, vols. I, II. Cambridge University Press, Cambridge 1979