Malkhaz Shashiashvili
Email: malkhaz@sms.edu.pk
Course: Probability Theory
Publications
1. M. A. Shashiashvili, Comparison of continuous and
discrete schemes in the problem of testing of two simple hypothesis, (Russian)
Uspekhi Math. Nauk, 32(1977), No 5.
2. V. M. Dochviri and M. A. Shashiashvili, On the convergence of costs in the
problem of optimal stopping of stochastic processes in the scheme of Kalman-Bucy,
Communic. Statistics-Sequential Analysis, 1(1982), No 3, 163-176.
3. R. N. Salia and M. A. Shashiashvili, On Palm's model with a large number
of machines and repairmen, Journal of the Royal statistical society, ser. B,
47(1985), No 2, 316-322.
4. M. A. Shashiashvili, On one semimartingale inequality for the Snell envelopes,
Theory of Probability and Applications, 37(1992), No 3, 592-593.
5. M. A. Shashiashvili, The Skorokhod oblique reflection problem in a convex
polyhedron, Georgian Math. J., 3(1996), No 2, 153-176.
6. M. A. Shashiashvili, On the excursion intervals away from the boundary for
the reflected Brownian motions, Proceedings of A. Razmadze Mathematical Institute,118(1998),
135-146.
7. B.Dochviri, M.Shashiashvili, On the characterization of costs in the optimal
stopping problem, Bulletin of the Georgian Acad. of sciences, 165 (2002), No
1.
8. B.Dochviri, M.Shashiashvili, On some new a priori estimates in the theory
of variational inequalities via stochastic analysis, Bulletin of the Georgian
Acad. of sciences, 165 (2002), No 2, 233-234.
9. G. Lominashvili and M. Shashiashvili, The approximation to the value function
of the optimal stopping problem on a finite time interval by discretized variational
inequalities, Proceedings of A. Razmadze Mathematical Institute, 128(2002),
79-100.
10. A. Danelia, B. Dochviri, M. Shashiashvili, Stochastic variational inequalities
and optimal stopping: applications to the robustness of the portfolio/consumption
processes, Stochastics and Stochastics Reports, 75 (2003), No 6, 407-423.
11. M. A. Shashiashvili, On one of Stefan’s problems, (Russian) Bulletin
of the Acad.sciences of the Georgian SSR, 78(1975), No 3, 557-560.
12. M. A. Shashiashvili, On the order of approximation problems of optimal stopping
for continuous-time Markov processes by discrete schemes, (Russian) Bulletin
of the Acad.sciences of the Georgian SSR, 84(1976), No 3, 529-532.
13. M. A. Shashiashvili, On the stochastic diferential representations for the
value functions in problems of optimal stopping for continuous parameter stochastic
processes, (Russian) Bulletin of the Acad.sciences of the Georgian SSR, 88(1977),
No 3, 533-536.
14. M. A. Shashiashvili, On the problem of optimal stopping for continuous parameter
stochastic processes, (Russian) Bulletin of the Acad. Sciences of the Georgian
SSR , 89(1978), No 1, 25-28.
15. M. A. Shashiashvili, On optimal stopping of continuous time stochastic processes
and the stochastic differential representations for the value functions, (Russian)
Lietuvos Matematikos Rinkinys,19(1979), No 1, 197-212.
16. M. A. Shashiashvili, Optimal stopping of well-measurable stochastic processes,
(Russian) Abstract of the dissertation of kandidat of Phys.-Math.sciences, Tbilisi,
1980.
17. V. M. Dochviri and M. A. Shashiashvili, On the convergence of costs in one
discrete problem of optimal stopping with partial observations, (Russian) Bulletin
of the Acad. Sciences of the Georgian SSR , 109(1983), No 1.
18. M. A. Shashiashvili, On the variation of the difference of singular components
in the Skorokhod problem and on stochastic differential systems in a half-space,
Stochastics, 24(1988), 151-169.
19. V. M. Dochviri and M. A. Shashiashvili, On sequential detection of the change
point of the Wiener process, (Russian) Statistical problems of control, 83(1988),
42-46.
20. M. A. Shashiashvili, On the weak convergence of the sequence of Markovian
networks of queues to the reflected in a half-space Gaussian diffusion process,
Fifth Intern. Vilnius Conf. on Probab. theory and Math. Statistics, (Russian)
Vilnius, Abstracts of communications, 4(1989), 364-365.
21. V. M. Dochviri and M. A. Shashiashvili, On a disorder problem with weighted
criterion, (Russian) Statistical problems of control, 89(1990), 120-123.
22. V. M. Dochviri and M. A. Shashiashvili, On optimal stopping of homogeneous
Markov process on the finite time interval, Math. Nachr, 156(1992), 269-281.
23. M. A. Shashiashvili, Semimartingale inequalities for the Snell envelopes,
Stochastics
and Stochastics Reports, 43(1993), 65-72.
24. M. A. Shashiashvili, A Lemma of variational distance between maximal functions
with application to the Skorokhod problem in a nonnegative orthant with state-dependent
reflection directions, Stochastics and stochastics Reports, 48(1994), 161-194.
25. M. A. Shashiashvili, On the Skorokhod oblique reflection problem, Reports
of Enlarged sessions of the seminar of I. Vekua. Institute of Applied Math.
10(1995), No 3, 82-91.
26. M. A. Shashiashvili, the Skorokhod oblique reflection problem in a convex
polyhedron and some applications, (Russian) Abstract of the dissertation of
Doctor of sciences (Physics and Mathematics), Tbilisi, 1995.
27. B. M. Dochviri and M. A. Shashiashvili, The American lookback put and optimal
stopping, Reports of Enlarged sessions of I. Vekua Inst. of Appl. Math. 18(1998),
23-25.
28. B.Dochviri, M.Shashiashvili, On the convergence of costs in the problem
of optimal stopping in the scheme of Kalman-Bucy, Reports of Enlarged Session
of the seminar of I. Vekua Insitute of Applied Mathematics, 15(2000), No 2,
47-49.
29. G. Lominashvili and M. Shashiashvili, The approximation to the value function
of the optimal stopping problem by discretized variational inequalities, Proceedings
of A. Razmadze Mathematical Institute, 122(2000), 125-136.
30. B.Dochviri, M.Shashiashvili, A priori estimates in the theory of variational
inequalities via stochastic analysis, Applied Mathematics and Informatics, 6
(2001), No 1, 30-44.
31. T. Abuladze, A. Danelia, B. Dochviri, M. Shashiashvili, The American lookback
call option, Bulletin of the Georgian Acad. of sciences, 165 (2002), No 1, 12-13.
32. A. Danelia, B. Dochviri, M. Shashiashvili, On new energy estimates for the
multidimensional obstacle problem, Memoirs on Differential Equations and Mathematical
Physics, 31 (2004), 15-34.