M-estimation for discretely observed ergodic diffusion processes with infinitely many jumps

Statistical Inference for Stochastic Processes

Volumn 9, Issue 2, 2006, Pages 179-225

  Shimizu, Yasutaka ^a  

^a OSAKA UNIVERSITY   (Japan)

Author keywords

Asymptotic normality; Diffusion process with jumps; Discrete observation; Infinitely many jumps; M estimation; Parametric inference; Partial efficiency

Indexed keywords

EID: 33745617674     PISSN: 13870874     EISSN: 15729311     Source Type: Journal    
DOI: 10.1007/s11203-005-8113-y     Document Type: Article

References (16)

1. Akritas, M. G. and Johnson, R. A.: Asymptotic inference in Levy processes of the discontinuous type, Ann. Statist. 9(3) (1981), 604-614.
2. Bichteler, K. and Jacod, J.: Calcul de Malliavin pour les diffusions avec sauts: existence d'une densite dans le cas unidimensionnel. Lecture Notes in Math. (1986). 132-157. Springer-Verlag. Berlin.
3. Genon-Catalot, V. and Jacod, J.: On the estimation of the diffusion coefficient for multidimensional diffusion process, Ann. Inst. Henri Poincaré Prob. Statist. 29 (1993), 119-151.
4. Ibragimov, I. A. and Has'minskii, R. Z.: Statistical Estimation, Springer-Verlag, Berlin, (1981).
5. Jacod, J. and Shiryaev, A. N.: Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin, (1987).
6. Kessler, M.: Estimation of diffusion processes from discrete observations, Scand. J. Statist. 24(1997), 211-229.
7. Kwon, Y.: Stability in distribution for a class of diffusion with jump, Bull. Korean Math. Soc. 34(2) (1997), 287-293.
8. Kwon, Y. and Lee, C.: Strong Feller property and irreducibility of diffusions with jumps, Stoch. Stoch. Rep. 67 (1999), 147-157.
9. Masuda, H.: On multi-dimensional Ornstein-Uhlenbeck processes driven by a general Levy process, Bernoulli. 10 (2004), 97-120.
10. Masuda, H.: Ergodicity and exponential β-mixing bounds for a strong solution of Lévy-driven stochastic differential equations, MHF preprint series, Kyushu University, (2004), 2004-2019.
11. Meyn, S. P. and Tweedie, R. L.: Stability of Markov processes II: continuous-time processes and sampled chains, Adv. Appl. Probab. 25 (1993), 487-517.
12. Meyn, S. P. and Tweedie, R. L.: Stability of Markov processes III: Foster-Lyapunov criteria for continuous-time processes, Adv. Appl. Probab. 24 (1993), 518-548.
13. Sørensen, M.: A note on the existence of a consistent maximum likelihood estimator for diffusions with jumps, In: Markov Process and Control Theory, Akademie-Verlag, Berlin, 1989, pp. 229-234.
14. Sørensen, M.: Likelihood methods for diffusions with jumps, Statistical Inference in Stochastic Processes, Marcel Dekker, New York, 1991, pp. 67-105.
15. Shimizu, Y. and Yoshida, N.: Estimation for diffusion processes with jumps from discrete observations, preprint, submitted (2002).
16. Woerner, J.: Statistical analysis for discretely observed Levy processes, Doctor thesis. (2001)