## Nanuli  Lazrieva

(21.12.1940 - 18.03.2019)

### List of Main Publications

1. A model of a problem of inventory theory with controlled initial flow. (Russian) Trudy Inst. Prikl. Mat. Tbiliss. Gos. Univ. 1 (1969), 227-233.

2. On construction of e-optimal stationary strategoes for thecontrolled diffusion processes. (Russian) Trudy Inst. Prikl. Mat. Tbiliss. Gos. Univ. 1 (1971), 281-289.

3. An estimation of the parameters of a Markov chain. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 61 (1971), 273-276 (with R. Chitashvili).

4. Optimal planning of water supply from reservoirs to head water intake structures of the main channals. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 75 (1974), No. 3, 673-676 (with D. Mamporia).

5. Optimal stopping in Markov processes with the restrictions on stopping rules. Preprints on the Stochastic Control Symposium, Budapest, Hungary, 1974, 85-87.

6. The solutions of the Wald-Bellman equation. (Russian) Litovsk. Mat. Sb. 14 (1974), no. 2, 79-88, 251.

7. The construction of a strong solution of a stochastic differential equation under the condition of instantaneous reflection on the boundary. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 95 (1979), no. 3, 549-552 (with R. Ja. Chitashvili).

8. Some properties of strong solutions of stochastic differential equations on an interval. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 97 (1980), no. 3, 553-556 (with R. Ja. Chitashvili).

9. Strong solutions of stochastic differential equations with boundary conditions. Stochastics 5 (1981), no. 4, 255-309 (with R. Chitashvili).

10. The existence of an $\epsilon$-optimal stationary strategy for controllable Markov processes with a general additive criterion. (Russian) Studies in probability theory and mathematical statistics, 75-96, Metsniereba, Tbilisi, 1982.

11. On conditions of weak convergence for a sequence of diffusion type processes. (Russian) Limit theorems and stochastic equations, Work Collect., Tbilisi, 1984, 82-97.

12. Weak convergence of semimartingales. Statistics and control of stochastic processes (Moscow, 1984), 251-276, Transl. Ser. Math. Engrg., Optimization Software, New York, 1985.

13. On the weak convergence of controlled semimartingales. Stochastic optimization (Kiev, 1984), 107-117, Lecture Notes in Control and Inform. Sci., 81, Springer, Berlin, 1986.

14. Asymptotic properties of the maximum likelihood estimator in a general scheme for a statistical experiment. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 123 (1986), no. 1, 25-28 (with T. Toronjadze).

15. The Itô-Ventsel formula for semimartingales and its application to recursive estimation. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 123 (1986), no. 2, 253-256 (with T. Toronjadze).

16.  Itô-Ventzel's formula for semimartingales, asymptotic properties of MLE and recursive estimation. Lecture Notes in Control and Information Sci., 96, 346-355. Springer-Verlag, Berlin, 1987 (with T. Toronjadze).

17. Asymptotic properties of the maximum likelihood estimator, Itô-Ventzel's formula for semimartingales and its application to the recursive estimation in a general scheme of statistical models. Proceedings of the 1st World Congress of the Bernoulli Society, Vol. 2 (Tashkent, 1986), 63-66, VNU Sci. Press, Utrecht, 1987 (with T. Toronjadze).

18. Joint asymptotic distribution of the maximum likelihood estimator and M-estimator. Probability theory and mathematical statistics (Kyoto, 1986), 259-266, Lecture Notes in Math., 1299, Springer, Berlin, 1988 (with T. Toronjadze).

19. Asymptotic properties of an M-estimate in a general statistical experiment scheme. (Russian) Statistics and control of random processes (Russian) (Preila, 1987), 105-112, "Nauka", Moscow, 1989 (with T. Toronjadze).

20. On asymptotic estimation theory with perturbation of a model in the general scheme of a statistical experiment. (Russian) Probability theory and mathematical statistics (Russian). Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 92 (1989), 106-145 (with R. Chitashvili and T. Toronjadze).

21. Asymptotic theory of M-estimators in general statistical models. Centre for Mathematics and Computer Sciences, Amsterdam, Netherlands, 1990, Report BS-R9019, 1-31 (with R. Chitashvili and T. Toronjadze).

22. Asymptotic theory of M-estimators in general statistical models. On asymptotic behaviour of estimators in the presence of nuisance parameters. Centre for Mathematics and Computer Sciences, Amsterdam, Netherlands, 1990, Report BS-R9020, 1-45 (with R. Chitashvili and T. Toronjadze).

23. On stable M-estimators in the partial likelihood scheme. New trends in probability and statistics, Vol. 1 (Bakuriani, 1990), 567-596, VSP, Utrecht, 1991 (with T. Toronjadze).

24. Robust estimators in statistical models with filtration. Shrinking neighbourhoods. Seminarberichte, Fachbereich Mathematik, Fernuniversität, Hagen, Germany 48 (1994), 50-68 (with T. Toronjadze).
25. The Robbins-Monro type stochastic differential equations. I.Convergence of solutions. Stochastics Stochastics Rep. 61 (1997), No. 1+2, 67-89 (with T. Sharia and T. Toronjadze).
26. Robust estimators in discrete time statistical models. Contiguous alternatives. Proc. A. Razmadze Math. Inst. 115 (1997), 59-96 (with T. Toronjadze).
27. Influence functionals for discrete time statistical models. Weakly contiguous alternatives. Proc. A. Razmadze Math. Inst. 115 (1997), 97-120 (with T. Toronjadze).
28. Robust estimators in statistical models associated with semimartingales. Proc. A. Razmadze Math. Inst. 118 (1998), 73-100 (with T. Toronjadze).
29. The Robbins-Monro type SDE and recursive estimation. Probability theory and mathematical statistics. Proceedings of the 7th international Vilnius conference, (ed. B. Grigelionis,  et al.) Vilnius, Lithuania, August, 12-18, 1998. TEV, Vilnius, 415-428 (1999) (with T. Toronjadze).
30. The semimartingale statistical models and robust estimation. Proc. of 4th Iranian International Statistical Conference 1 (1999), 261-303 (with T. Toronjadze).
31. The Polyak weighted averaging procedure for Robbins-Monro type SDE.  Proc. A. Razmadze Math. Inst. 124 (2000), 115-130 (with T. Toronjadze).
32. Continuous semimartingale with small noise. CULAN estimates of multidimensional  parameter. Bull. Georgian Acad. Sci. 168 (2003), No. 2 (with G. Meladze and T. Toronjadze).
33. Continuous semimartingale with small noise. Construction of optimal B-robust estimates of multidimensional  parameter. Bull. Georgian Acad. Sci. 168 (2003), No. 3 (with G. Meladze and T. Toronjadze).
34. General M-estimators in the presence of nuisance parameter. Some projections technique. Georgian Math. J. 10 (2003), No. 2, 271-288 (with T. Toronjadze).
35. The Robbins-sMonro type stochastic differential equations. II. Asymptotic behavior of solutions. Stochastics Stochastics Rep. 75 (2003), No. 3, 153-180 (with T. Sharia and T. Toronjadze).
36. The change-point problem for continuous martingales. Proc. A. Razmadze Math. Inst. 137 (2005), 39-63 (with T. Kavtaradze and M. Mania).
37. A Bayesian-martingale approach to the general disorder problem. Stochastic Process. Appl. 117 (2007), no. 8, 1093-1120 (with T. Kavtaradze, M. Mania and P. Muliere)
38. Semimartingale stochastic approximation procedure and recursive estimation. Martingale theory and its application. J. Math. Sci. (N.Y.) 153 (2008), no. 3, 211-261 (with T. Sharia and T. Toronjadze)
39. Optimal robust mean-variance hedging in incomplete financial markets. Martingale theory and its application. J. Math. Sci. (N.Y.) 153 (2008), no. 3, 262-290 (with T. Toronjadze).
40. The Robbins-Monro type stochastic differential equations. III. Polyak's averaging. Stochastics 82 (2010), no. 1-3, 165-188 (with T. Toronjadze)
41. Recursive parameter estimation in the trend coefficient of a diffusion process. Georgian Math. J. 17 (2010), no. 4, 683-704 (with T. Toronjadze).
42. Recursive estimation procedures for one-dimensional parameter of statistical models associated with semimartingales.Trans. A. Razmadze Math. Inst. 171 (2017), no. 1, 57-75 (with T. Toronjadze)