- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 748376, 8 pages
Least Squares Estimation for -Fractional Bridge with Discrete Observations
Department of Mathematics, Anhui Normal University, Wuhu 241000, China
Received 15 November 2013; Accepted 7 December 2013; Published 23 January 2014
Academic Editor: Litan Yan
Copyright © 2014 Guangjun Shen and Xiuwei Yin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- F. Biagini, Y. Hu, B. Øksendal, and T. Zhang, Stochastic Calculus for fBm and Applications. Probability and Its Application, Springer, Berlin, Germany, 2008.
- Y. Hu, “Integral transformations and anticipative calculus for fractional Brownian motions,” Memoirs of the American Mathematical Society, vol. 175, no. 825, 2005.
- Y. S. Mishura, Stochastic Calculus for Fractional Brownian Motion and Related Processes, vol. 1929 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2008.
- D. Nualart, The Malliavin Calculus and Related Topics, Springer, Berlin, Germany, 2nd edition, 2006.
- K. Es-Sebaiy and I. Nourdin, “Parameter estimation for α fractional bridges,” in Malliavin Calculus and Stochastic Analysis: A Festschrift in Honor of David Nualart, F. Viens, J. Feng, Y. Hu, and E. Nualart, Eds., vol. 34 of Springer Proceedings in Mathematics and Statistics, pp. 385–412, 2013.
- M. Barczy and G. Pap, “Asymptotic behavior of maximum likelihood estimator for time inhomogeneous diffusion processes,” Journal of Statistical Planning and Inference, vol. 140, no. 6, pp. 1576–1593, 2010.
- M. Barczy and G. Pap, “-Wiener bridges: singularity of induced measures and sample path properties,” Stochastic Analysis and Applications, vol. 28, no. 3, pp. 447–466, 2010.
- C. A. Tudor and F. G. Viens, “Statistical aspects of the fractional stochastic calculus,” The Annals of Statistics, vol. 35, no. 3, pp. 1183–1212, 2007.
- Y. Hu and D. Nualart, “Parameter estimation for fractional Ornstein-Uhlenbeck processes,” Statistics & Probability Letters, vol. 80, no. 11-12, pp. 1030–1038, 2010.
- R. Belfadli, K. Es-Sebaiy, and Y. Ouknine, “Parameter estimation for fractional Ornstein-Uhlenbeck processes: non-ergodic case,” Frontiers in Science and Engineering, vol. 1, pp. 1–16, 2011.
- Y. Hu and J. Song, “Parameter estimation for fractional Ornstein-Uhlenbeck processes with discrete observations,” in Malliavin Calculus and Stochastic Analysis: A Festschrift in Honor of David Nualart, F. Viens, J. Feng, Y. Hu, and E. Nualart, Eds., vol. 34 of Springer Proceedings in Mathematics and Statistics, pp. 427–442, 2013.
- K. Es-Sebaiy, “Berry-Esséen bounds for the least squares estimator for discretely observed fractional Ornstein-Uhlenbeck processes,” Statistics & Probability Letters, vol. 83, no. 10, pp. 2372–2385, 2013.
- E. Alòs, O. Mazet, and D. Nualart, “Stochastic calculus with respect to Gaussian processes,” The Annals of Probability, vol. 29, no. 2, pp. 766–801, 2001.
- V. Pipiras and M. S. Taqqu, “Integration questions related to fractional Brownian motion,” Probability Theory and Related Fields, vol. 118, no. 2, pp. 251–291, 2000.
- E. Alòs and D. Nualart, “Stochastic integration with respect to the fractional Brownian motion,” Stochastics and Stochastics Reports, vol. 75, no. 3, pp. 129–152, 2003.