Geodesic
Asymptotic behavior of parametric estimation for a class of nonlinear diffusion process
Zhu, Chenglian 1
1 School of Mathematical Science, Huaiyin Normal University, Huaian, Jiangsu 223300, P. R. China
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 6, p. 778-784.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, a stochastic process, which is a class of nonhomogeneous diffusion process from the perspective of the corresponding nonlinear stochastic differential equation is studied. The parameter included in the drift term are estimated by sequential maximum likelihood methodology. The sequential estimators are proved to be closed, unbiased, strongly consistent, normally distributed, and optimal in the mean square sense.
DOI : 10.22436/jnsa.011.06.05
Classification : 60F15
Keywords: Nonlinear diffusion process, sequential maximum likelihood estimation, mean square sense

Zhu, Chenglian  1

1 School of Mathematical Science, Huaiyin Normal University, Huaian, Jiangsu 223300, P. R. China 
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Zhu, Chenglian . Asymptotic behavior of parametric estimation for a class of nonlinear diffusion process. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 6, p. 778-784. doi : 10.22436/jnsa.011.06.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.06.05/

[1] Bishwal, J. P. N. Parameter estimation in stochastic differential equations, Lecture Notes in Mathematics, Springer, New York, 2008 | DOI

[2] Bo, L.; Yang, X. Sequential maximum likelihood estimation for reflected generalized Ornstein-Uhlenbeck processes, Statist. Probab. Lett., Volume 82 (2012), pp. 1374-1382 | DOI | Zbl

[3] Hu, Y.; Lee, C. Parameter estimation for a reflected fractional Brownian motion based on its local time, J. Appl. Probab., Volume 50 (2013), pp. 592-597 | DOI | Zbl

[4] Karatzas, I.; Shreve, S. E. Brownian motion and stochastic calculus, Springer-Verlag, New York, 1991 | DOI

[5] Kuang, N.; Xie, H. Sequential maximum likelihood estimation for the hyperbolic diffusion process, Methodol. Comput. Appl. Probab., Volume 17 (2015), pp. 373-381 | DOI | Zbl

[6] Kutoyants, Y. A. Statistical inference for ergodic diffusion processes, Springer-Verlag, London, 2004 | DOI

[7] Lee, C.; Bishwal, J. P. N.; Lee, M. H. Sequential maximum likelihood estimation for reflected Ornstein-Uhlenbeck processes, J. Statist. Plann. Inference, Volume 142 (2012), pp. 1234-1242 | Zbl | DOI

[8] Lee, C.; J. Song On drift parameter estimation for reflected fractional Ornstein-Uhlenbeck processes, Stochastics, Volume 88 (2016), pp. 751-778 | DOI | Zbl

[9] Liptser, R. S.; Shiryayev, A. N. Statistics of random processes I , General Theory, Springer-Verlag, New York, 1977 | DOI

[10] Liptser, R. S.; A. N. Shiryayev Statistics of random processes II, Applications, Springer-Verlag, New York, 1977 | DOI

[11] A. A. Novikov Sequential estimation of the parameters of diffusion processes (Russian), Mat. Zametki, Volume 12 (1972), pp. 627-638

[12] Rao, B. L. S. Prakasa Statistical inference for diffusion type processes, Oxford University Press , New York, 1999

[13] Revuz, D.; Yor, M. Continuous martingales and brownian motion, Third edition, Springer-Verlag, Berlin, 1999

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