Statistical inference for Vasicek-type model driven by self-similar Gaussian processes

References

• Belfadli, R., K. Es-Sebaiy, and Y. Ouknine. 2011. Parameter estimation for fractional Ornstein-Uhlenbeck processes: Non-ergodic case. Frontiers in Science and Engineering (An International Journal Edited by Hassan II Academy of Science and Technolo2 1:1–16.
   Google Scholar
• El Machkouri, M., K. Es-Sebaiy, and Y. Ouknine. 2016. Least squares estimator for nonergodic Ornstein-Uhlenbeck processes driven by gaussian processes. Journal of the Korean Statistical Society 45 (3):329–41.
   Web of Science ®Google Scholar
• Houdré, C., and J. Villa. 2003. An example of infinite dimensional quasi-helix. Contemporary mathematics. American Mathematical Society 336:195–C201.
   Google Scholar
• Hu, Y., and D. Nualart. 2010. Parameter estimation for fractional Ornstein-Uhlenbeck processes. Statistics and Probability Letters 80 (11–12):1030–8.
   Web of Science ®Google Scholar
• Kleptsyna, M., and A. Le Breton. 2002. Statistical analysis of the fractional Ornstein-Uhlenbeck type process. Statistical Inference for Stochastic Processes 5 (3):229–41.
   Google Scholar
• Kloeden, P., and A. Neuenkirch. 2007. The pathwise convergence of approximation schemes for stochastic differential equations. LMS Journal of Computation and Mathematics 10:235–53.
   Google Scholar
• Maejima, M., and C. A. Tudor. 2007. Wiener integrals with respect to the hermite process and a non-Central limit theorem. Stochastic Analysis and Applications 25 (5):1043–56.
   Web of Science ®Google Scholar
• Mendy, I. 2013. Parametric estimation for Sub-fractional ornstein-uhlenbeck process. Journal of Statistical Planning and Inference 143 (4):663–74.
   Web of Science ®Google Scholar
• Nourdin, I. 2012. Selected aspects of fractional Brownian motion. Bocconi and Springer Series 4. Springer, Milan: Bocconi University Press.
   Google Scholar
• Nourdin, I., D. Nualart, and R. Zintout. 2016. Multivariate Central limit theorems for averages of fractional Volterra processes and applications to parameter estimation. Statistical Inference for Stochastic Processes 19 (2):219–34.
   Google Scholar
• Nourdin, I., and D. Tran. 2018. Statistical inference for Vasicek-type model driven by hermite processes. Stochastic Processes and their Applications. doi:10.1016/j.spa.2018.10.005.
   PubMed Web of Science ®Google Scholar
• Nualart, D. 2006. The Malliavin calculus and related topics. volume Second Edition. Berlin: Springer.
   Google Scholar
• Russo, F., and C. Tudor. 2006. On bifractional Brownian motion. Stochastic Processes and Their Applications 116 (5):830–56.
   Web of Science ®Google Scholar
• Shen, G., X. Yin, and L. Yan. 2016. Least squares estimation for Ornstein-Uhlenbeck processes driven by the weighted fractional brownian motion. Acta Mathematica Scientia 36 (2):394–408.
   Web of Science ®Google Scholar
• Shen, G., and L. Yan. 2014. An approximation of Sub-fractional Brownian motion. Communications in Statistics-Theory and Methods 43 (9):1873–86.
   Web of Science ®Google Scholar
• Shen, G., and Q. Yu. 2017. Least squares estimator for Ornstein-Uhlenbeck processes driven by fractional lévy processes from discrete observations. Statistical Papers doi:10.1007/s00362-017-0918-4.
   PubMed Web of Science ®Google Scholar
• Tanaka, K. 2013. Distributions of the maximum likelihood and minimum contrast estimators associated with the fractional Ornstein-Uhlenbeck process. Statistical Inference for Stochastic Processes 16 (3):173–92.
   Google Scholar
• Tanaka, K. 2015. Maximum likelihood estimation for the non-ergodic fractional Ornstein-Uhlenbeck process. Statistical Inference for Stochastic Processes 18 (3):315–32.
   Google Scholar
• Tran, D. 2017. Non-Central limit theorems for quadratic functionals of hermite-driven long memory moving average processes. Stochastics and Dynamics 18 (4):1850028.
   Web of Science ®Google Scholar
• Tudor, C. 2007. Some properties of the Sub-fractional brownian motion. Stochastics: An International Journal of Probability and Stochastic Processes 79 (5):431–48.
   Google Scholar
• Tudor, C., and F. Viens. 2007. Statistical aspects of the fractional stochastic calculus. The Annals of Statistics 35 (3):1183–212.
   Web of Science ®Google Scholar
• Tudor, C. 2013. Analysis of variations for self-similar processes. A stochastic calculus approach. Probability and its applications (New York). Cham: Springer.
   Google Scholar
• Xiao, W., and J. Yu. 2017. Asymptotic theory for estimating drift parameters in the fractional Vasicek model. Econometric Theory, doi:10.1017/S0266466618000051.
   Google Scholar
• Xiao, W., W. Zhang, and W. Xu. 2011. Parameter estimation for fractional Ornstein-Uhlenbeck processes at discrete observation. Applied Mathematical Modelling 35 (9):4196–207.
   Web of Science ®Google Scholar
• Xiao, W., X. Zhang, and Y. Zuo. 2018. Least squares estimation for the drift parameters in the Sub-fractional Vasicek processes. Journal of Statistical Planning and Inference 197:141–155. doi:10.1016/j.jspi.2018.01.003.
   Web of Science ®Google Scholar
• Yan, L., and G. Shen. 2010. On the collision local time of Sub-fractional Brownian motions. Statistics and Probability Letters 80 (5–6):296–308.
   Web of Science ®Google Scholar
• Young, L. C. 1936. An inequality of the hölder type connected with stieltjes integration. Acta Mathematica 67:251–82.
   Google Scholar