Initially scientific interests were defined by the problems of Markov sufficient statistics in the theory of the optimal stopping of stochastic processes, that led to the concepts of predictable characteristics of semimartigales and compensators of stochastic point measures, martingale characterisation of stochastic processes, stochastic integral representation of local martingales and non-linear filtering equations. Explicit formulas for local densities, criteria of contiguity and weak convergence of probability measures are also based on the same martingale techniques. special attention was paid to the stochastic processes with values on the manifolds with boundaries.

A new trend was determined by the construction and investigation of non-Gausian self-similar stochastic processes and fields as well as polygonal Markov fields. The convergence to self-similar fields appears in stochastic hydrodynamics, statistics, etc.

The theory of optimal control of general solutions to stochastic Itô's equations and boundary value problems for the related integer-differential Bellman's equation defined one of the most important areas of the activity of the department.

Extensions of the classical law of large numbers, the law of iterated logarithms, the central limit
theorem, asymptotic expansions of remainder terms and the probabilities of large deviations to
the case of Banach space-valued random variables, worked out at the department, are motivated by
the theory of empirical processes, *U*-statistics, and other applications.

Recent **scientific interests** of the department are also connected with the asymptotic
spectral properties of random operators, statistical manifolds of solutions of martingale problems,
the general theory of stochastic evolution equations, mathematical problems solutions of finance
and the risk theory, time series with long range dependence, analysis of functions with finite
*p*-variation.

**Scientific staff:**

Dr. Arvydas ASTRAUSKAS, senior researcher

Dr. Stasys CEPULENAS, researcher

Dr. Liudas GIRAITIS, senior research associate

Dr. Remigijus Petras GYLYS, researcher

Dr. habil. Kestutis KUBILIUS, principal research associate

Dr. Remigijus LEIPUS, senior researcher

Dr.habil.Remigijus MIKULEVICIUS, principal research associate

Doc., Dr. Rimas NORVAISA, senior researcher

Dr. Saulius NORVIDAS, senior researcher

Dr. habil. Henrikas PRAGARAUSKAS, principal research associate, vice director of Institute

Dr.habil. Liudas STUPELIS, senior research associate

**Contact person: **

Prof., Dr.habil Bronius Grigelionis

Head of Mathematical Statistics Department

**Address:**

Mathematical Statistics Department

Institute of Mathematics and Informatics

Akademijos 4, Vilnius 2600, Lithuania

**Phone:** +(370 5) 21 09 730

**Fax:** +(370 5) 27 29 209

**E-mail: **broniusg@ktl.mii.lt

Last updated on October 11, 2002