On the estimation of the diffusion coefficient for multi-dimensional diffusion processes
Annales de l'I.H.P. Probabilités et statistiques, Volume 29 (1993) no. 1, pp. 119-151.
@article{AIHPB_1993__29_1_119_0,
     author = {Genon-Catalot, Valentine and Jacod, Jean},
     title = {On the estimation of the diffusion coefficient for multi-dimensional diffusion processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {119--151},
     publisher = {Gauthier-Villars},
     volume = {29},
     number = {1},
     year = {1993},
     zbl = {0770.62070},
     mrnumber = {1204521},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1993__29_1_119_0/}
}
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
DA  - 1993///
SP  - 119
EP  - 151
VL  - 29
IS  - 1
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1993__29_1_119_0/
UR  - https://zbmath.org/?q=an%3A0770.62070
UR  - https://www.ams.org/mathscinet-getitem?mr=1204521
LA  - en
ID  - AIHPB_1993__29_1_119_0
ER  - 
%0 Journal Article
%A Genon-Catalot, Valentine
%A Jacod, Jean
%T On the estimation of the diffusion coefficient for multi-dimensional diffusion processes
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1993
%P 119-151
%V 29
%N 1
%I Gauthier-Villars
%G en
%F AIHPB_1993__29_1_119_0
Genon-Catalot, Valentine; Jacod, Jean. On the estimation of the diffusion coefficient for multi-dimensional diffusion processes. Annales de l'I.H.P. Probabilités et statistiques, Volume 29 (1993) no. 1, pp. 119-151. http://www.numdam.org/item/AIHPB_1993__29_1_119_0/

[1] D.J. Aldous, Stopping times and tightness, Ann. Probab., Vol. 6, 1978, pp. 335-340. | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[7] G. Dohnal, On estimating the diffusion coefficient, J. Appl. Prob., Vol. 24, 1987, pp. 105-114. | MR | Zbl

[8] P. Feigin, Asymptotic theory of conditional inference for stochastic processes, Stochastic Proc. Appl., Vol. 22, 1985, pp. 89-102. | MR | Zbl

[9] D. Florens-Zimrou, Approximate discrete-time schemes for statistics of diffusion processes, Statistics, Vol. 20, 1989, pp. 547-557. | MR | Zbl

[10] J. Hajek, A characterization of limiting distributions of regular estimates, Z.für Warsch. Theo. Geb., Vol. 14, 1970, pp. 324-330. | MR | Zbl

[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. | MR | Zbl

[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.

[14] P. Hall and C. Heyde, Martingale limit theory and its applications, Academic Press; New York, 1980. | MR | Zbl

[15] J. Jacod, Random sampling in estimation problems for continuous Gaussian processes with independent increments, Stoch. Processes and Appl., 1993 (to appear). | MR | Zbl

[16] J. Jacod and A.N. Shiryaev, Limit theorems for stochastic processes, Springer Verlag; Berlin, 1987. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[20] L. Le Cam and G.L. Yang, Asymptotics in Statistics, Springer Verlag, Berlin, 1990. | MR | Zbl

[21] R.S. Liptser and A.N. Shiryayev, Statistics of random processes, I. General theory, Springer Verlag, Berlin, 1977. | MR | Zbl

[22] S. Molchanov, Diffusion processes and Riemannian geometry, Russ. Math. Survey, Vol. 30, 1975, pp. 1-63. | MR | Zbl

[23] D.W. Stroock and S.R.S. Varadhan, Multidimensional diffusion processes, Springer Verlag, Berlin, 1979. | MR | Zbl