Thèmes de recherche

Processus à sauts, Systèmes de particules, Statistique des diffusions et des diffusions à sauts, Marches aléatoires en milieu aléatoire

Habilitation à diriger des recherches

Théorèmes limites dans le cadre markovien. Application aux statistiques, soutenue le 6 juillet 2010.

Publications

1. F. Comets, O.Loukianov, D. Loukianova (2022) Limit of the environment viewed from Sinaï's walk. en révision Télécharger
2. X. Erny, E. Löcherbach, D. Loukianova (2021) Strong error bounds for the convergence to its mean field limit for systems of interacting neurons in a diffusive scaling. AAP à paraître Télécharger
3. X. Erny, E. Löcherbach, D. Loukianova (2021) Conditional propagation of chaos for mean field systems of interacting neurons. Electron. J. Probab. 26 1 - 25, 2021. Télécharger
4. X. Erny, E. Löcherbach, D. Loukianova (2019) Mean field limits for interacting Hawkes processes in a diffusive regime. Accepted at Bernoulli. Télécharger
5. X. Erny, E. Löcherbach, D. Loukianova (2021) White-noise driven conditional McKean-Vlasov limits for systems of particles with simultaneous and random jumps, preprint Télécharger
6. Gloter,A., Honoré, I. Loukianova, D. Non-asymptotic concentration inequality for an approximation of the invariant distribution of a diffusion driven by a compound Poisson process, ESAIM:PS Volume 24, 2020, pp: 883-913. Télécharger
7. Gloter, A., Mai, H., Loukianova, D., Jump filtering and efficient drift estimation for Lévy-driven SDEs, The Annals of Statistics Volume 46, Number 4 (August 2018), 1445-1480. Télécharger
8. Comets, F., Falconnet, M., Loukianova, D., Loukianov, O., Maximum likelihood estimator consistency for recurrent random walk in a parametric random environment with finite support. Stochastic Processes and their Applications, vol.126, Issue 11, November 2016, pp. 3578-3604 Télécharger
9. Andréolétti, P., Loukianova, D., Matias, C., Hidden Markov model for parameter estimation of a random walk in a Markov environment. ESAIM Prob.& Stat.19:605-625, 2015. Télécharger
10. Falconnet, M., Gloter, A., Loukianova, D., MLE in the context of a sub-balistic random walk in a parametric random environment, Mathematical Methods of Statistics, à paraître. Télécharger
11. Falconnet, M., Loukianova, D., Matias, C., Central limit theorem for maximum likelihood estimator for ballistic random walk in a parametric random environment, Mathematical Methods of Statistics, Jul.2014, Vol23, Iss.3, pp.159-175 Télécharger
12. Comets, F., Falconnet, M., Loukianova, D., Loukianov. O., Matias, C., Maximum likelihood estimator consistency for ballistic random walk in a parametric random environment, Stochastic Processes and their Applications, vol. 124, pp. 268-288, 2014. Télécharger
13. Löcherbach, E., Loukianova, D., Loukianov. O., Spectral condition, hitting times and Nash inequality, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, vol. 50, n. 4, pp. 1213-1230, 2014. Télécharger
14. Löcherbach, E., Loukianova, D., Polynomial deviation bounds for recurrent Harris processes having general state space, ESAIM Probabilité et statistique, vol.17, pp. 195-218, 2013. Télécharger
15. Löcherbach, E., Loukianova, D.(2009). Deviation inequalities for centered additive functionals of recurrent Harris processes having general state space, Journal of Theoretical Probability, vol. 25, pp. 231-261, 2012. Télécharger
16. Loukianov, O., Loukianova, D., Song, S., Poincaré inequality and exponential integrability of hitting times for a linear diffusion, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, vol. 47, pp. 679 - 698, 2011. Télécharger
17. Löcherbach, E., Loukianova, D., Loukianov, O., Polynomial bounds in the Ergodic theorem for positive recurrent one-dimensional diffusions and integrability of hitting times, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, vol.47, pp. 425-449, 2011. Télécharger
18. Löcherbach, E., Loukianova, D., Loukianov, O.,Penalized nonparametric drift estimation for ergodic diffusion, ESAIM, Probability and Statistics, vol. 15, pp. 197-216, 2011 Télécharger
19. Löcherbach E., Loukianova D., Loukianov O. (2011) Penalized nonparametric drift estimation for ergodic diffusion, ESAIM Probability and Statistics 15, 197-216. Télécharger
20. Löcherbach, E., Loukianova, D., The law of iterated logarithm for additive functionals and martingale additive functionals of Harris recurrent Markov processes, Stochastic Processes and their Applications, vol. 119, Issue 7, pp. 2312-2335, 2009. Télécharger
21. Löcherbach, E., Loukianova, D., On Nummelin Splitting for continuous time Harris recurrent Markov processes and application to kernel estimation for multidimensional diffusions, Stochastic Processes and their Applications, vol.118, pp. 1301-1321, 2008. Télécharger
22. Loukianov, O., Loukianova, D., Uniform deterministic equivalent of AF of recurrent diffusions and non-parametric drift estimation, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, vol. 44, No 4, pp.771-186, 2008. Télécharger
23. Loukianov, O., Loukianova, D., Deterministic equivalents of additive functionals of recurrent diffusions and drift estimation, Statistical Inference for stochastics processes, vol.11, issue 2, pp. 107-121, 2008. Télécharger
24. Loukianov, O., Loukianova, D., Almost sure rate of convergence of MLE for multidimensional diffusions, Lecture Notes in Statistics , vol. 187, pp. 329-349, 2005
25. Loukianov, O., Loukianova, D., Uniform law of large numbers and consistency of estimators for Harris diffusions, Statistics and Probability Letters, vol. 34, pp. 347-355, 2005. Télécharger
26. Loukianova, D. Remark on semigroup technics and the MLE estimations, Staistics and Probability Letters, vol. 62, pp. 111-115, 2003
27. Loukianova, D., Lower bound on the restitution error in the Hopfield Model, Probability Theory and Related Fields, vol. 107, pp. 161-176, 1998
28. Loukianova, D., Capacité de mémoire dans le modèle de Hopfield. CRAS t.318, Série 1, pp. 157-160, 1994

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