LABORATORY 16

Laboratory of Stochastic Dynamical Systems

Head of Laboratory – Dr.Sc. (Mathematics), Prof. Aleksandr Veretennikov

Tel.: (095) 299-94-15; E-mail: veretenn@iitp.ru

 

The leading researchers of the laboratory include:

Dr.Sc. (Math.)

V. Kalashnikov

Dr.

P. Kitsul

Dr.Sc. (Techn.)

R. Liptser

Dr.

A. Puhalskii

Dr.

F. Grigoriev

Dr.

A. Serebrovskii

Dr.

O. Gulinsky

Dr.

S. Lototsky

Dr.

V. Kistlerov

    

Currently R. Liptser, P. Kitsul, A. Puhalskii and S. Lototsky are working abroad remaining the staff members of Laboratory.

 

 

Directions of Activity and MAIN RESULTS

In 1998-99 the Laboratory continued research investigations in the following directions.

1. Stochastic analysis: Limit theorems for Markov processes, semimartingales, and other stochastic processes – A. Veretennikov, R. Liptser, O. Gulinsky, A. Puhalskii, A. Serebrovskii, V. Kalashnikov.

New large deviation, rare event, moderate deviations, diffusion approximation and convergence rate results were obtained for Markov processes, random sums, random walks, semimartingales, queues, risk processes, and queueing networks.

2. Mathematical Statistics: A. Veretennikov, A. Puhalskii, R. Liptser.

Large and moderate deviation results and convergence rate results were applied to complex parametric and non-parametric inference problems.

3. Optimal Control for moving objects: F. Grigoriev.

New control and synthesis results were obtained for certain classes of nonlinear moving objects; the number of switching was studied.

4. Functional Programming and Language Development – V. Kistlerov.

Semantics of functional programming languages was studied on the base of FLAC language.

Teaching:

International collaboration. Fruitful collaboration is established with the probability group of the LATP CMI Universite de Provence, Marseille, France, and, in particular, with Professor Etienne Pardoux as its leader.

We also have close contacts with Universite Paris 6 (Professors Jean Jacod and Pierre Priouret); Universite du Main in France (Professor Yuri Kutoyants); Weierstrass Institute for Applied Analysis and Stochastics – WIAS, Berlin, Germany; the Univerity of Warwick, UK (Professor David Elworthy); Mathematical Institute of the University of Copenhagen; University of Trier (Professor Dieter Baum); University of Wuerzburg (Professor Elart von Collani), and some others.

Conferences. The staff members participated in 1998-99 to several International and Russian Conferences in China – F. Grigoriev, Russia, Lithuania and France – A. Veretennikov, Germany, Latvia – V. Kalashnikov. A. Veretennikov was an invited speaker in Vilnius, Lithuania, 7th Conference on Probab. Theory Mathem. Statistics and a co-organiser of a mini-workshop during that meeting; V. Kalashnikov was a Chairman of the Organizing Committee of the Conference on Rare Events in Riga, Latvia, and a member of Organizing Committees of the International Conferences “Stability Problems for Stochastic Models” (September 1999, Poland) and “Distributed Computer Communication Networks” (November 1999, Israel). Many talks were given in Universities of Europe and US – A. Puhalskii, V. Kalashnikov, O. Gulinsky, A. Veretennikov.

Other activities. V. Kalashnikov is an Associate Editor in the journals: “Queueing Systems. Theory and Applications”; “Stochastic Models”; “Pattern Recognition and Image Analysis”; “Fundamental and Applied Mathematics”. A. Veretennikov is an Associate Editor in the journal “Stochastic Processes and their Applications”.

 

Grants from:

A. Veretennikov.

 

Publications in 1999

  1. Григорьев Ф.Н., Кузнецов Н.А. Синтез оптимального управления для одного подвижного объекта. Тезисы докладов 26-й Всероссийской конференции по управлению движением морскими судами и специальными аппаратами. М.: ИПУ РАН, 1999, с. 12-15.

    2.  

  2. Григорьев Ф.Н., Кузнецов Н.А. Оптимальное по быстродействию управление в одной нелинейной задаче. Тезисы докладов Международной конференции по проблемам управления. М.: Фонд "Проблемы управления", 1999, т. 1, с. 124-126.

  3. Grigoriev F.N., Grigorieva E.N. Dependence of functional groups on depolymerization of coal organic matter. PROSPECTS FOR COAL SCIENCE IN THE 21th CENTURY, ed. Bao Qing Li and Zhen Yu Liu. Shanxi Science & Technology Рress, Taiwan, P.R. China, 1999, p. 251-254.

  4. Gulinsky O.V., Liptser R.Sh. An example of large deviations for a stationary process. Theory Probab. Appl., 1999, 44(1), p. 211-225.

  5. Kalashnikov V. Bounds for ruin probabilities in the presence of large claims and their comparison. North American Actuarial Journal, 1999, v. 3, no. 2, p. 116-129.

  6. Kalashnikov V., Tsitsiashvili G. Tails of waiting times and their bounds. Queueing Systems, 1999, no. 32, p. 257-283.

  7. Калашников В.В., Цициашвили Г.Ш. Двусторонние оценки случайных сумм с субэкспоненциальными слагаемыми. Проблемы передачи информации, 1999, т. 35, № 3, с. 67-79.

  8. Kalashnikov V.V., Enikeeva F., Rusaityte D. Continuity estimates for ruin probabilities. Preprint of Copenhagen Univ., No 157, Lab. of Actuarial Math., February 1999.

  9. Еникеева Ф., Калашников В.В., Русайтите Д. Оценки непрерывности вероятностей разорения для марковско-модулированного процесса риска. Теория вероятностей и ее применения, 1999, т. 44, № 2, с. 171-172.

  10. Kalashnikov V.V., Bon J.-L. Some estimates of geometric sums. Universite de Paris-Sud, Prepublication 99.35, 1999.

  11. Kalashnikov V., Tsitsiashvili G. Accuracy estimates for asymptotics of random sums with subexponential summands. Probabilistic analysis of Rare Events: Theory and Problems of Safety, Insurance and Ruin. Proceedings of the International Conference (28 June – 3 July 1999, Riga, Latvia). Riga Aviation University, Riga, 1999, p. 29-35.

  12. Kalashnikov V., Enikeeva F., Rusaityte D. Continuity of ruin probabilities. Probabilistic analysis of Rare Events: Theory and Problems of Safety, Insurance and Ruin. Proceedings of the International Conference (28 June – 3 July 1999, Riga, Latvia). Riga Aviation University, Riga, 1999, p. 56-62.

  13. Kalashnikov V. Random service process may lead to heavy-tailed waiting times. Distributed Computer Communication Networks. Proceedings of the International Conference (November 1999, Tel-Aviv, Israel). Institute for Information Transmission Problems, Moscow, 1999, p. 63-67.

  14. Kalashnikov V., Norberg R. Power tailed ruin probabilities in the presence of risky investments. Preprint of Copenhagen Univ., No. 159, December 1999, Laboratory of Actuarial Mathematics.

  15. Kalashnikov V., Konstantinides D. A simple proof of a result of Asmussen. Preprint of Copenhagen Univ., No. 160, December 1999, Laboratory of Actuarial Mathematics.

  16. Puhalskii A. Large deviations of semimartingales: a maxingale problem approach, I. Limits as solutions to a maxingale problem, Stochastics Stoch. Rep. 1997, no. 61, p. 141-243; II. Uniqueness for the maxingale problem. Applications, Stochastics Stoch. Rep., 1999, 63.

  17. Puhalskii A. Moderate Deviations for Queues in Critical Loading. Queueing Systems, 1999, 31(3-4), p. 359-392.

  18. Серебровский А.П., Клепцина М.Л. Принципы больших уклонений для условных распределений диффузионных процессов. Проблемы передачи информации, 1999, т. 35, № 2, с. 83-89.

  19. Veretennikov A.Yu. On large deviations in the averaging principle for SDE's with a "full dependence". Ann. Probab. 1999, 27(1), p. 284-296.

  20. Веретенников А. Ю. О полиномиальном перемешивании и скорости сходимости для стохастических дифференциальных и разностных уравнений. Теория вероятностей и ее применения, 1999, т. 44, № 2, с. 312-327.

  21. Kistlerov V. An Operational Semantics of Suspended Computations. Samara, 1999.

  22. Кистлеров В. Интенсионалы частичных Функций и построение значений. Екатеринбург, Философский конгресс “Философские основания математики и информатики”,