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:
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