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

How to cite

top

Genon-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. [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

Citations in EuDML Documents

top
  1. Shota Gugushvili, Peter Spreij, Consistent non-parametric bayesian estimation for a time-inhomogeneous brownian motion
  2. Arnaud Gloter, Jean Jacod, Diffusions with measurement errors. I. Local asymptotic normality
  3. Emmanuel Gobet, LAN property for ergodic diffusions with discrete observations
  4. Arnaud Gloter, Jean Jacod, Diffusions with measurement errors. I. Local Asymptotic Normality
  5. Arnaud Gloter, Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient
  6. Arnaud Gloter, Jean Jacod, Diffusions with measurement errors. II. Optimal estimators
  7. Masayuki Uchida, Nakahiro Yoshida, Estimation for misspecified ergodic diffusion processes from discrete observations
  8. Arnak Dalalyan, Nakahiro Yoshida, Second-order asymptotic expansion for a non-synchronous covariation estimator
  9. Marc Hoffmann, On estimating the diffusion coefficient : parametric versus nonparametric
  10. Arnaud Gloter, Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.