Regularization and integral representations of Hermite processes

Statistics and Probability Letters

Volumn 80, Issue 23-24, 2010, Pages 2014-2023

  Pipiras, Vladas ^a,b   Taqqu, Murad S ^c  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b UNIVERSITY OF NORTH CAROLINA   (United States)

^c BOSTON UNIVERSITY   (United States)

Author keywords

Fractional Brownian motion; Hermite processes; Multiple Wiener It integrals; Regularization; Stochastic Fubini theorem

Indexed keywords

EID: 77958513205     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2010.09.008     Document Type: Article

References (20)

1. Albin J.M.P. A note on Rosenblatt distributions. Statistics & Probability Letters 1998, 40(1):83-91.
2. Biagini F., Hu Y., Øksendal B., Zhang T. Stochastic Calculus for Fractional Brownian Motion and Applications. Probability and its Applications (New York) 2008, Springer-Verlag London Ltd., London.
3. Breton J.-C., Nourdin I. Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion. Electronic Communications in Probability 2008, 13:482-493.
4. Chronopoulou A., Tudor C.A., Viens F.G. Application of Malliavin calculus to long-memory parameter estimation for non-Gaussian processes. Comptes Rendus Mathématique. Académie des Sciences. Paris 2009, 347(11-12):663-666.
5. Chronopoulou, A., Viens, F.G., Tudor, C.A., 2010. Self-similarity parameter estimation and reproduction property for non-Gaussian Hermite processes. Preprint. Available at: arxiv:0807.1208.
6. Dobrushin R.L., Major P. Non-central limit theorems for nonlinear functionals of Gaussian fields. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1979, 50(1):27-52.
7. Theory and Applications of Long-Range Dependence 2003, Birkhäuser Boston Inc., Boston, MA. P. Doukhan, G. Oppenheim, M.S. Taqqu (Eds.).
8. León J.A. Fubini theorem for anticipating stochastic integrals in Hilbert space. Applied Mathematics and Optimization. An International Journal with Applications to Stochastics 1993, 27(3):313-327.
9. Mishura Y.S. Stochastic Calculus for Fractional Brownian Motion and Related Processes. Lecture Notes in Mathematics 2008, vol. 1929. Springer-Verlag, Berlin.
10. Molchan G.M. Historical comments related to fractional Brownian motion. Theory and Applications of Long-Range Dependence 2003, 39-42. Birkhäuser Boston, Boston, MA. P. Doukhan, G. Oppenheim, M.S. Taqqu (Eds.).
11. Nourdin, I., Nulart, D., Tudor, C.A., 2007. Central and non-central limit theorems for weighted power variations of fractional Brownian motion. Preprint. Available at: arxiv:0710.5639.
12. Nualart D. The Malliavin Calculus and Related Topics. Probability and its Applications (New York) 2006, Springer-Verlag, Berlin. second ed.
13. Peccati G., Taqqu M.S. Wiener Chaos: Moments, Cumulants and Diagrams. Bocconi & Springer Series 2010, vol. 1. Springer.
14. Pipiras V. Wavelet-type expansion of the Rosenblatt process. The Journal of Fourier Analysis and Applications 2004, 10(6):599-634.
15. Rosenblatt M. Independence and dependence. Proc. 4th Berkeley Sympos. Math. Statist. and Prob. 1961, vol. II:431-443. Univ. California Press, Berkeley, Calif.
16. Slud E.V. The moment problem for polynomial forms in normal random variables. The Annals of Probability 1993, 21(4):2200-2214.
17. Taqqu M.S. Weak convergence to fractional Brownian motion and to the Rosenblatt process. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1975, 31:287-302.
18. Taqqu M.S. Convergence of integrated processes of arbitrary Hermite rank. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1979, 50(1):53-83.
19. Taqqu, M.S., 2011. The Rosenblatt process. In: Davis, R., Lii, K.-S., Politis, D., (Eds.), Selected Works of Murray Rosenblatt, Springer Verlag, New York (in press).
20. Tudor C.A. Analysis of the Rosenblatt process. ESAIM. Probability and Statistics 2008, 12:230-257.