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DIRECTIONS OF SCIENTIFIC ACTIVITY:
Filtering, interpolation, extrapolation, recognition of stochastic processes, transmission of stochastic signals trough continuous and discrete channels with memory; detection of anomalous noises; mathematical theory of financial analysis.
MAIN RESULTS:
For a case of population of continuous and discrete in time observations with arbitrary multiplicity memory:
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Basic equation of nonlinear generalized moving extrapolation with moving memory (BENGMEMM) has been obtained. BENGMEMM defines joint a posteriori density of values for unobserved process at the end of observations, at times characterizing memory, and future times which are moments of extrapolation (forecast, prediction) process.
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Synthesis of filter-interpolator-extrapolator defining optimal mean-square sense for estimate of filtering, interpolation and extrapolation has been carried out in conditions of a posteriori gaussianity on the basis of BENGMEMM using method of semi-invariant function.
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Joint synthesis of optimal in mean-square sense of unbiased filter-interpolator-extrapolator in case of continuous and discrete observations with arbitrary multiplicity memory when anomalous noises are present has been carried out and its properties have been examined.
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A solution for a problem of finding a posteriori probabilities of hypothesis and likelihood ratio in common problem of hypothesis arbitrary number recognition on population of continuous and discrete observations for both fixed and moving arbitrary multiplicity memory has been obtained.
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A problem for detection of anomalous noises with pre-set structure effect of its component to components of observation vector has been solved and algorithm potential properties relatively to lower bounds of false detection probabilities and gap of anomalous noise have been examined.
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An equation for joint amount of information about current and past values for unobserved process in common and conventionally-Gaussian cases has been obtained, e.g. from informative point of view a joint problem for continuous and discrete filtering and interpolation in case of continuous and discrete observations with fixed arbitrary multiplicity memory has been considered.
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An equation for joint amount of information about current and future values for unobserved process in general and conventionally-Gaussian cases has been obtained, e.g. from informative point of view joint problem of continuous and discrete filtering and interpolation in case of continuous and discrete observations with fixed arbitrary multiplicity memory has been considered.
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The problem for optimal continuous and discrete transmission of diffuse Gaussian and Markovian signal through channel with memory and with lag given instantaneous noiseless feedback has been solved and the research for effectiveness of optimal transmission methods has been carried out.
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Problems of research of effectiveness for observations with memory relatively to observations without memory and observations with memory relatively to observations with gap in problems of filtering, interpolation, extrapolation, anomalous noises detection, information effectiveness of observations and optimal transmission have been solved.
SCIENTIFIC PUBLICATIONS:
Author and coauthor of more than 150 scientific papers, including 3 monographs, 10 tutorials.
GUIDANCE OF MASTER’S DEGREE STUDENTS, POSTGRADUATES AND DOCTORAL CANDIDATES:
Postgraduate – Danilyuk Elena Yurievna
Successful defense of dissertation on topic:
«Financial market data processing and taking decision on structure of European option» In candidacy for a degree in physical and mathematical sciences.
The defense took place during the meeting of dissertation council Д 212.267.12 in Tomsk State University on March 4, 2015.
GRANT ACTIVITY:
The federal target program «Scientific and teaching staff of innovative Russia» (activity 1.5)
2010-2011: «Analytic and algebraic methods of information processing, group theory and control in stochastic systems», state registration number ГК 10.347.с.2010;
2012-2013: «Modern methods of optimization and analysis, group theory and its applications in information processing, mathematical models of physics and economics», state registration number state registration number;
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