On the estimation of the diffusion coefficient for multi-dimensional diffusion processes

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1. [1] D.J. Aldous, Stopping times and tightness, Ann. Probab., Vol. 6, 1978, pp. 335-340. Zbl0391.60007MR474446
2. [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. [3] G. Courtadon, Une synthèse des modèles d'évaluation d'options sur obligations, Finance, 6, Vol. 2, 1985. , 
4. [4] D. Dacunha-Castelle and M. Duflo, Probabilités et statistiques II, Masson; Paris, 1983. Zbl0535.62004MR732786
5. [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. [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. [7] G. Dohnal, On estimating the diffusion coefficient, J. Appl. Prob., Vol. 24, 1987, pp. 105-114. Zbl0615.62109MR876173
8. [8] P. Feigin, Asymptotic theory of conditional inference for stochastic processes, Stochastic Proc. Appl., Vol. 22, 1985, pp. 89-102. Zbl0611.62105MR852385
9. [9] D. Florens-Zimrou, Approximate discrete-time schemes for statistics of diffusion processes, Statistics, Vol. 20, 1989, pp. 547-557. Zbl0704.62072MR1047222
10. [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. [11] V. Genon-Catalot, Thèse, Université Paris-Sud, Orsay, 1987. 
12. [12] V. Genon-Catalot, Maximum contrast estimation for diffusion processes from discrete observations, Statistics, Vol. 21, 1990, pp. 99-116. Zbl0721.62082MR1056065
13. [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. [14] P. Hall and C. Heyde, Martingale limit theory and its applications, Academic Press;New York, 1980. Zbl0462.60045MR624435
15. [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. [16] J. Jacod and A.N. Shiryaev, Limit theorems for stochastic processes, Springer Verlag;Berlin, 1987. Zbl0635.60021MR959133
17. [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. [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. [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. [20] L. Le Cam and G.L. Yang, Asymptotics in Statistics, Springer Verlag, Berlin, 1990. Zbl0719.62003MR1066869
21. [21] R.S. Liptser and A.N. Shiryayev, Statistics of random processes, I. General theory, Springer Verlag, Berlin, 1977. Zbl0364.60004MR474486
22. [22] S. Molchanov, Diffusion processes and Riemannian geometry, Russ. Math. Survey, Vol. 30, 1975, pp. 1-63. Zbl0315.53026MR413289
23. [23] D.W. Stroock and S.R.S. Varadhan, Multidimensional diffusion processes, Springer Verlag, Berlin, 1979. Zbl0426.60069MR532498

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