On the estimation of the diffusion coefficient for multi-dimensional diffusion processes
Valentine Genon-Catalot; Jean Jacod
Annales de l'I.H.P. Probabilités et statistiques (1993)
- Volume: 29, Issue: 1, page 119-151
- ISSN: 0246-0203
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topGenon-Catalot, Valentine, and Jacod, Jean. "On the estimation of the diffusion coefficient for multi-dimensional diffusion processes." Annales de l'I.H.P. Probabilités et statistiques 29.1 (1993): 119-151. <http://eudml.org/doc/77447>.
@article{Genon1993,
author = {Genon-Catalot, Valentine, Jacod, Jean},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {multidimensional diffusion processes; LAMN property; diffusion coefficient; drift; non-anticipative functional; local asymptotic mixed normality; conditional centered Gaussian variable},
language = {eng},
number = {1},
pages = {119-151},
publisher = {Gauthier-Villars},
title = {On the estimation of the diffusion coefficient for multi-dimensional diffusion processes},
url = {http://eudml.org/doc/77447},
volume = {29},
year = {1993},
}
TY - JOUR
AU - Genon-Catalot, Valentine
AU - Jacod, Jean
TI - On the estimation of the diffusion coefficient for multi-dimensional diffusion processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1993
PB - Gauthier-Villars
VL - 29
IS - 1
SP - 119
EP - 151
LA - eng
KW - multidimensional diffusion processes; LAMN property; diffusion coefficient; drift; non-anticipative functional; local asymptotic mixed normality; conditional centered Gaussian variable
UR - http://eudml.org/doc/77447
ER -
References
top- [1] D.J. Aldous, Stopping times and tightness, Ann. Probab., Vol. 6, 1978, pp. 335-340. Zbl0391.60007MR474446
- [2] R. Azencott, Densité des diffusions en temps petit : développements asymptotiques (partie I), Sém. Proba. XVIII, 1984, pp. 402-498; Lect. Notes in Math., n° 1059, Springer Verlag; Berlin. Zbl0546.60079MR770974
- [3] G. Courtadon, Une synthèse des modèles d'évaluation d'options sur obligations, Finance, 6, Vol. 2, 1985. ,
- [4] D. Dacunha-Castelle and M. Duflo, Probabilités et statistiques II, Masson; Paris, 1983. Zbl0535.62004MR732786
- [5] D. Dacunha-Castelle and D. Florens-Zmirou, Estimation of the coefficient of a diffusion from discrete observations, Stochastics, Vol. 19, 1986, pp. 263-284. Zbl0626.62085MR872464
- [6] A.Ja. Dorogovcev, The consistency of an estimate of a parameter of a stochastic differential equation, Theory Probab. and Math. Statist. Vol. 10, 1976, pp. 73-82. Zbl0394.62064
- [7] G. Dohnal, On estimating the diffusion coefficient, J. Appl. Prob., Vol. 24, 1987, pp. 105-114. Zbl0615.62109MR876173
- [8] P. Feigin, Asymptotic theory of conditional inference for stochastic processes, Stochastic Proc. Appl., Vol. 22, 1985, pp. 89-102. Zbl0611.62105MR852385
- [9] D. Florens-Zimrou, Approximate discrete-time schemes for statistics of diffusion processes, Statistics, Vol. 20, 1989, pp. 547-557. Zbl0704.62072MR1047222
- [10] J. Hajek, A characterization of limiting distributions of regular estimates, Z.für Warsch. Theo. Geb., Vol. 14, 1970, pp. 324-330. Zbl0193.18001MR283911
- [11] V. Genon-Catalot, Thèse, Université Paris-Sud, Orsay, 1987.
- [12] V. Genon-Catalot, Maximum contrast estimation for diffusion processes from discrete observations, Statistics, Vol. 21, 1990, pp. 99-116. Zbl0721.62082MR1056065
- [13] V. Genon-Catalot and J. Jacod, On the diffusion of the diffusion coefficient for diffusion processes: random sampling, Preprint # 100, Lab. Probabilités, Univ. Paris-VI, 1992. Zbl0804.62078
- [14] P. Hall and C. Heyde, Martingale limit theory and its applications, Academic Press;New York, 1980. Zbl0462.60045MR624435
- [15] J. Jacod, Random sampling in estimation problems for continuous Gaussian processes with independent increments, Stoch. Processes and Appl., 1993 (to appear). Zbl0806.62065MR1200407
- [16] J. Jacod and A.N. Shiryaev, Limit theorems for stochastic processes, Springer Verlag;Berlin, 1987. Zbl0635.60021MR959133
- [17] P. Jeganathan, On the asymptotic theory of estimation when the limit of the loglikelihood is mixed normal, Sankya, Series A, Vol. 44, 1982, pp. 173-212. Zbl0584.62042MR688800
- [18] P. Jeganathan, Some asymptotic properties of risk functions when the limit of the experiment is mixed normal, Sankya, Series A, Vol. 45, 1983, pp. 66-87. Zbl0574.62035MR749355
- [19] R.A. Kasonga, The consistency of a non-linear least-squares estimate from diffusion processes, Stoch. Processes and Appl., Vol. 30, 1988, pp. 263-275. Zbl0662.62092
- [20] L. Le Cam and G.L. Yang, Asymptotics in Statistics, Springer Verlag, Berlin, 1990. Zbl0719.62003MR1066869
- [21] R.S. Liptser and A.N. Shiryayev, Statistics of random processes, I. General theory, Springer Verlag, Berlin, 1977. Zbl0364.60004MR474486
- [22] S. Molchanov, Diffusion processes and Riemannian geometry, Russ. Math. Survey, Vol. 30, 1975, pp. 1-63. Zbl0315.53026MR413289
- [23] D.W. Stroock and S.R.S. Varadhan, Multidimensional diffusion processes, Springer Verlag, Berlin, 1979. Zbl0426.60069MR532498
Citations in EuDML Documents
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- Arnaud Gloter, Jean Jacod, Diffusions with measurement errors. I. Local asymptotic normality
- Emmanuel Gobet, LAN property for ergodic diffusions with discrete observations
- Arnaud Gloter, Jean Jacod, Diffusions with measurement errors. I. Local Asymptotic Normality
- Arnaud Gloter, Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient
- Arnaud Gloter, Jean Jacod, Diffusions with measurement errors. II. Optimal estimators
- Masayuki Uchida, Nakahiro Yoshida, Estimation for misspecified ergodic diffusion processes from discrete observations
- Arnak Dalalyan, Nakahiro Yoshida, Second-order asymptotic expansion for a non-synchronous covariation estimator
- Marc Hoffmann, On estimating the diffusion coefficient : parametric versus nonparametric
- Arnaud Gloter, Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient
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