Wiener Integrals with Respect to the Hermite Process and a Non-Central Limit Theorem

REFERENCES

• Albin , J.M.P. 1998 . A note on the Rosenblatt distributions . Statistics and Probability Letters 40 ( 1 ): 83 – 91 .
   Web of Science ®Google Scholar
• Albin , J.M.P. 1998 . On extremal theory for self similar processes . Annals of Probability 26 ( 2 ): 743 – 793 .
   Web of Science ®Google Scholar
• Alos , E. , and Nualart , D. 2003 . Stochastic integration with respect to the fractional Brownian motion . Stochastics and Stochastics Reports 75 : 129 – 152 .
   Google Scholar
• Alos , E. , Mazet , O. , and Nualart , D. 2001 . Stochastic calculus with respect to Gaussian processes . Ann. Prob. 29 : 766 – 801 .
   Web of Science ®Google Scholar
• Bilingsley , P. 1968. Convergence of Probability Measures . Wiley , New York.
   Google Scholar
• Cheridito , P. , Kawaguchi , H. , and Maejima , M. 2003 . Fractional Ornstein–Uhlenbeck processes . Elect. J. Prob. 8 : 1 – 14 .
   Google Scholar
• Davydov , Y.A. 1970 . The invariance principle for stationary processes . Theory of Probability and its Applications 15 : 487 – 498 .
   Web of Science ®Google Scholar
• Decreusefond , L. , and Ustunel , A.S. 1998 . Stochastic analysis of the fractional Brownian motion . Potential Analysis 10 : 177 – 214 .
   Web of Science ®Google Scholar
• Dobrushin , R.L. , and Major , P. 1979 . Non-central limit theorems for non-linear functionals of Gaussian fields . Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 50 : 27 – 52 .
   Web of Science ®Google Scholar
• Embrechts , P. , and Maejima , M. 2002 . Selfsimilar Processes . Princeton University Press .
   Google Scholar
• Duncan , T. , Hu , Y.Z. , and Pasik-Duncan , B. 2000 . Stochastic calculus for fractional Brownian motion I. Theory . SIAM Journal on Control and Optimization 38 ( 2 ): 582 – 612 .
   Web of Science ®Google Scholar
• Kasahara , Y. , and Maejima , M. 1986 . Functional limit theorems for weughted sums od i.i.d. random variables . Probability Theory and Related Fields 72 : 161 – 183 .
   Web of Science ®Google Scholar
• Kasahara , Y. , and Maejima , M. 1988 . Weighted sums of i.i.d. random variables attracted to integrals of stable processes . Probability Theory and Related Fields 78 : 75 – 96 .
   Web of Science ®Google Scholar
• Nualart , D. 1995 . Malliavin Calculus and Related Topics . Springer .
   Google Scholar
• Pipiras , V. 2004 . Wavelet type expansion of the Rosenblatt process . Journal of Fourier Analysis and Applications 10 ( 6 ): 599 – 634 .
   Web of Science ®Google Scholar
• Pipiras , V. 2005 . Wavelet-based simulation of fractional Brownian motion revisited . Applied and Computational Harmonic Analysis 19 ( 1 ): 49 – 60 .
   Web of Science ®Google Scholar
• Pipiras , V. , and Taqqu , M.S. 2000 . Convergence of weighted sums of random variables with long range dependence . Stochastic Processes and their Applications 90 : 157 – 174 .
   Web of Science ®Google Scholar
• Pipiras , V. , and Taqqu , M.S. 2001 . Integration questions related to the fractional Brownian motion . Probability Theory and Related Fields 118 : 251 – 281 .
   Web of Science ®Google Scholar
• Rosenblatt , M. 1960 . Independence and dependence . In Proceedings of the 4th Berkeley Symposium on Mathematical Statistics . II . 431 – 443 .
   Google Scholar
• Taqqu , M.S. 1975 . Weak convergence to the fractional Brownian motion and to the Rosenblatt process . Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 31 : 287 – 302 .
   Web of Science ®Google Scholar
• Taqqu , M.S. 1979 . Convergence of integrated processes of arbitrary Hermite rank . Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 50 : 53 – 83 .
   Web of Science ®Google Scholar