Estimation of change point for switching fractional diffusion processes

References

• E.Alos, O.Mazet, and D.Nualart, Stochastic calculus with respect to Gaussian processes, Ann. Prob.29 (2001), pp. 766–801.
   Web of Science ®Google Scholar
• P.Billingsley, Convergence of Probability Measures, Wiley, New York, 1968.
   Google Scholar
• E.Carlstein, H.G.Muller, and D.Siegmund, Change-point Problems, Institute of Mathematical Statistics Lecture Notes, Monograph Series,Vol. 23, Institute of Mathematical Statistics, Hayward, CA, 1994.
   Google Scholar
• H.Chernoff and H.Rubin, The estimation of the location of a discontinuity in density, Proceedings of the Third Berkeley Symposium Mathematical Statistics and Probability, Vol. 1, University of California Press, Berkeley, pp. 19–37, 1955.
   Google Scholar
• M.Csorgo and L.Horvath, Limit Theorems on Change-point Analysis, Wiley, New York, 1997.
   Google Scholar
• A.De Gregorio and S.M.Iacus, Least squares volatility change point estimation for partially observed diffusion processes, Commun. Stat. Theory Methods37 (2008), pp. 2342–2357.
   Web of Science ®Google Scholar
• J.Deshayes and D.Picard, Lois asymptotiques des test et estimateurs de rupture dans un modelle statistique classique, Ann. Inst. H. Poincare Sect. II20 (1984), pp. 309–327.
   Google Scholar
• Y.Hu and D.Nualart, Parameter estimation for fractional Ornstein–Uhlenbeck processes, Stat. Prob. Lett.80 (2010), pp. 1030–1038.
   Web of Science ®Google Scholar
• Y.Hu, D.Nualart, W.Xiao, and W.Zhang, Exact maximum likelihood estimator for drift fractional Brownian motion at discrete time, Acta Math. Sci.31 (2011), pp. 1851–1859.
   Web of Science ®Google Scholar
• S.M.Iacus and N.Yoshida, Numerical analysis of volatility change point estimators for discretely sampled stochastic differential equations, Econ. Notes39 (2010), pp. 107–127.
   Google Scholar
• S.M.Iacus and N.Yoshida, Estimation for the change point of the volatility in a stochastic differential equation, Stoch. Process. Appl.122 (2012), pp. 1068–1092.
   Web of Science ®Google Scholar
• I.A.Ibragimov and R.Z.Has'minskii, Statistical Estimation: Asymptotic Theory, Springer-Verlag, New York, 1981.
   Google Scholar
• M.L.Kleptsyna and A.Le Breton, Statistical analysis of the fractional Ornstein–Uhlenbeck type process, Stat. Infer. Stoch. Process5 (2002), pp. 229–248.
   Google Scholar
• M.L.Kleptsyna, A.Le Breton, and M.C.Roubaud, Parameter estimation and optimal filtering for fractional type stochastic systems, Stat. Infer. Stoch. Process.3 (2000), pp. 173–182.
   Google Scholar
• Yu.A.Kutoyants, Parameter Estimation for Stochastic Processes, Trans. and Ed. B.L.S. Prakasa Rao,Heldermann-Verlag, Berlin, 1984.
   Google Scholar
• Yu.A.Kutoyants, Identification of Dynamical Systems with Small Noise, Kluwer, Dordrecht, 1994.
   Google Scholar
• Yu.A.Kutoyants, Statistical Inference for Ergodic Diffusion Processes, Springer-Verlag, London, 2004.
   Google Scholar
• M.R.Leadbetter, G.Lindgren, and H.Rootzen, Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag, New York, 1983.
   Google Scholar
• S.Lee, Y.Nishiyama, and N.Yoshida, Test for parameter change in diffusion processes by cusum statistics based on one-step estimators, Ann. Inst. Stat. Math.58 (2006), pp. 211–222.
   Web of Science ®Google Scholar
• M.Matsui and N.-R.Shieh, On the exponentials of fractional Ornstein–Uhlenbeck processes, Electr. J. Prob.14 (2009), pp. 594–611.
   Web of Science ®Google Scholar
• I.Norros, E.Valkeila, and J.Virtamo, An elementary approach to a Girsanov type formula and other analytical results on fractional Brownian motion, Bernoulli5 (1999), pp. 571–587.
   Web of Science ®Google Scholar
• D.Nualart and A.Rascanu, Differential equations driven by fractional Brownian motion, Collect. Math.53 (2002), pp. 55–81.
   Google Scholar
• K.R.Parthasarathy, Probability Measures on Metric Spaces, Academic Press, London, 1967.
   Google Scholar
• B.L.S.Prakasa Rao, Estimation of the location of the cusp of a continuous density, Ann. Math. Stat.39 (1968), pp. 76–87.
   Google Scholar
• B.L.S.Prakasa Rao, Asymptotic Theory of Statistical Inference, Wiley, New York, 1987.
   Google Scholar
• B.L.S.Prakasa Rao, Statistical Inference for Diffusion Type Processes, Arnold/Oxford University Press, London/New York, 1999.
   Google Scholar
• B.L.S.Prakasa Rao, Statistical Inference for Fractional Diffusion Processes, Wiley, Chichester, 2010.
   Google Scholar
• D.Revuz and M.Yor, Continuous Martingales and Brownian Motion, Springer-Verlag, Berlin, 1999.
   Google Scholar
• S.G.Samko, A.A.Kilbas, and O.I.Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science, Yverdon, 1993.
   Google Scholar
• J.Song and S.Lee, Test for parameter change in discretely observed diffusion processes, Stat. Infer. Stoch. Process.12 (2009), pp. 165–183.
   Google Scholar
• W.Xiao, W.Zhang, and W.Xu, Parameter estimation for fractional Ornstein–Uhlenbeck processes at discrete observation, Appl. Math. Model.35 (2011), pp. 4196–4207.
   Web of Science ®Google Scholar