Infinite Variation Tempered Stable Ornstein–Uhlenbeck Processes with Discrete Observations

References

• Baeumer , B. , Meerschaert , M. M. ( 2010 ). Tempered stable Lévy motion and transit super-diffusion . Journal of Computational and Applied Mathematics 233 ( 10 ): 2438 – 2448 .
   Web of Science ®Google Scholar
• Barndorff-Nielsen , O. E. , Shephard , N. ( 2001 ). Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics (with discussion) . Journal of the Royal Statistical Society B 63 ( 2 ): 167 – 241 .
   Google Scholar
• Benth , F. E. , Gorth , M. , Kufakunesu , R. ( 2007 ). Valuing volatility and variance swaps for a non-Gaussian Ornstein–Uhlenbeck stochastic volatility model . Applied Mathematical Finance 14 ( 4 ): 347 – 363 .
   Google Scholar
• Brockwell , P. J. , Davis , R. A. , Yang , Y. ( 2007 ). Estimation for nonnegative Lévy-driven Ornstein–Uhlenbeck processes . Journal of Applied Probability 44 ( 4 ): 977 – 989 .
   Web of Science ®Google Scholar
• Chambers , J. M. , Mallows , C. L. , Stuck , B. W. ( 1976 ). A method for simulating stable random variables . Journal of the American Statistical Association 71 ( 354 ): 340 – 344 .
   Web of Science ®Google Scholar
• Devroye , L. ( 2009 ). Random variate generation for exponential and polynomially tilted stable distributions. ACM Transactions on Modeling and Computer Simulation 19(4):Article No. 18 .
   Google Scholar
• Imai , J. , Kawai , R. ( 2010 ). On finite truncation of infinite shot noise series representation of tempered stable laws. Preprint
   Google Scholar
• Jongbloed , G. , van der Meulen , F. H. , van der Vaart , A. W. ( 2005 ). Nonparametric inference for Lévy-driven Ornstein–Uhlenbeck processes . Bernoulli 11 ( 5 ): 759 – 791 .
   Web of Science ®Google Scholar
• Kawai , R. , Masuda , H. ( 2009 ). Exact simulation of finite variation tempered stable Ornstein–Uhlenbeck processes, available at http://hdl.handle.net/2324/15635 .
   Google Scholar
• Kawai , R. , Masuda , H. ( 2011 ). On simulation of tempered stable random variates . Journal of Computational and Applied Mathematics 235 ( 8 ): 2873 – 2887 .
   Web of Science ®Google Scholar
• Masuda , H. ( 2004 ). On multidimensional Ornstein–Uhlenbeck processes driven by a general Lévy process . Bernoulli 10 ( 1 ): 1 – 24 .
   Web of Science ®Google Scholar
• Michael , J. R. , Schucany , W. R. , Haas , R. W. ( 1976 ). Generating random variates using transformations with multiple roots . The American Statistician 30 : 88 – 90 .
   Web of Science ®Google Scholar
• Rosiński , J. ( 2001 ). Series representations of Lévy processes from the perspective of point processes . In: Barndorff-Nielsen , O.-E. , Mikosch , T. , Resnick , S. I. , eds. Lévy Processes - Theory and Applications . Boston : Birkhäuser , pp. 401 – 415 .
   Google Scholar
• Rosiński , J. ( 2007 ). Tempering stable processes . Stochastic Processes and Their Applications 117 ( 6 ): 677 – 707 .
   Web of Science ®Google Scholar
• Sato , K. ( 1999 ). Lévy Processes and Infinitely Divisible Distributions . Cambridge : Cambridge University Press .
   Google Scholar
• Sun , S. , Zhang , X. ( 2009 ). Empirical likelihood estimation of discretely sampled processes of OU type . Science in China Series A: Mathematics 52 ( 5 ): 908 – 931 .
   Google Scholar
• Tweedie , M. C. K. ( 1984 ). An index which distinguishes between some important exponential families , In: Ghosh , J. , Roy , J. , eds. Statistics: Applications and New Directions: Proc. Indian Statistical Institute Golden Jubilee International Conference , pp. 579 – 604 .
   Google Scholar
• Zhang , S. , Zhang , X. ( 2008 ). Exact simulation of IG-OU processes . Methodology and Computing in Applied Probability 10 ( 3 ): 337 – 355 .
   Web of Science ®Google Scholar
• Zhang , S. , Zhang , X. ( 2009 ). On the transition law of tempered stable Ornstein–Uhlenbeck processes . Journal of Applied Probability 46 ( 3 ): 721 – 731 .
   Web of Science ®Google Scholar
• Zolotarev , V. M. ( 1986 ). One-Dimensional Stable Distributions . Providence , RI : American Mathematical Society .
   Google Scholar