Exponential Ergodicity and β-Mixing Property for Generalized Ornstein-Uhlenbeck Processes

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References

[1] L. de Haan and R. L. Karandikar, “Embedding a Stochastic Difference Equation in a Continuous Time Process,” Stochastic Processes and Their Applications, Vol. 32, No. 2, 1989, pp. 225-235.
doi:10.1016/0304-4149(89)90077-X

[2] D. B. Nelson, “ARCH Models as Diffusion Approximations,” Journal of Econometrics, Vol. 45, No. 1-2, 1990, pp. 7-38. doi:10.1016/0304-4076(90)90092-8

[3] C. Klüppelberg, A. Lindner and R. A. Maller, “A Continuous Time GARCH Process Driven by a Levy Process: Stationarity and Second Order Behavior,” Journal of Applied Probability, Vol. 41, No. 3, 2004, pp. 601-622.
doi:10.1239/jap/1091543413

[4] O. E. Barndorff-Nielsen and N. Shephard, “Non-Gaussian Ornstein-Uhlenbeck Based Models and Some of Their Uses in Financial Economics (with dis-cussion),” Journal of Royal Statistical Society, Series B, Vol. 63, No. 2, 2001, pp. 167-241. doi:10.1111/1467-9868.00282

[5] R. A. Maller, G. Müller and A. Szimayer, “GARCH Modeling in Continuous Time for Irregularly Spaced Time Series Data,” Bernoulli, Vol. 14, No. 2, 2008, pp. 519-542. doi:10.3150/07-BEJ6189

[6] A. Lindner and R. A. Maller, “Levy Integrals and the Stationarity of Generalized Ornstein-Uhlenbeck Processes,” Stochastic Processes and Their Applications, Vol. 115, No. 10, 2005, pp. 1701-1722.
doi:10.1016/j.spa.2005.05.004

[7] V. Fasen, “Asymptotic Results for Sample Auto-covariance Functions and Extremes of Integrated Generalized Ornstein-Uhlenbeck Processes,” 2010.
http://www.ma.tum.de/stat/

[8] H. Masuda, “On Multidimen-sional Ornstein-Uhlenbeck Processes Driven by a General Levy Process,” Bernoulli, Vol. 10, No. 1, 2004, pp. 97-120.
doi:10.3150/bj/1077544605

[9] C. Klüppelberg, A. Lindner and R. A. Maller, “Continuous Time Volatility Modeling: COGARCH versus Ornstein-Uhlenbeck Models,” In: Y. Ka-banov, R. Liptser, and J. Stoyanov, Eds., Stochastic Calculus to Mathematical Finance, The Shiryaev Festschrift, Springer, Berlin, 2006, pp. 393-419.
doi:10.1007/978-3-540-30788-4_21

[10] A. Lindner, “Continuous Time Approximations to GARCH and Stochastic Volatility Models,” In: T. G. Andersen, R. A. Davis, J. P. Krei and T. Mikosch, Eds., Handbook of Financial Time Series, Springer, Berlin, 2010.

[11] S. P. Meyn and R. L. Tweedie, “Markov Chain and Stochastic Stability,” Springer-Verlag, Berlin, 1993.

[12] J. Bertoin, “Lévy Processes,” Cambridge University Press, Cambridge, 1996.

[13] K. Sato, “Levy Processes and Infinitely Divisible Distributions,” Cambridge University Press, Cambridge, 1999.

[14] P. Tuominen and R. L. Tweedie, “Exponential Decay and Ergodicity of General Markov Processes and Their Discrete Skeletons,” Advances in Applied Probability, Vol. 11, 1979, pp.784-803. doi:10.2307/1426859

[15] G. H. Hardy, J. E. Littlewood and G. Pólya, “Inequalities,” Cambridge University Press, Cambridge, 1952.

[16] J. Liu and E. Susko, “On Strict Stationarity and Ergodicity of a Nonlinear ARMA Model,” Journal of Applied Probability, Vol. 29, 1992, pp. 363-373.
doi:10.2307/3214573

[17] R. L. Tweedie, “Drift Conditions and Invariant Measures for Markov Chains,” Stochastic Processes and their Applications, Vol. 92, No. 2, 2001, pp. 345-354.
doi:10.1016/S0304-4149(00)00085-5

[18] K. Sato and M. Yamazato, “Operator-self Decomposable Distributions as Limit Distributions of Processes of Ornstein-Uhlenbeck Type,” Stochastic Processes and Their Applications, Vol. 17, No. 1, 1984, pp. 73-100.
doi:10.1016/0304-4149(84)90312-0