# Yuriy Kozachenko

 POSITION Professor of the Department of Probability, Statistics and Actuarial Mathematics WORK EXPERIENCE 1964–1967 Postgraduate Student Instute of Mathematics of National Academy of Sciences of Ukraine, Kyiv (Ukraine) 1967–1976 Lecturer Taras Shevchenko National University of Kyiv, Kyiv (Ukraine) 1976–1987 Assistant professor Taras Shevchenko National University of Kyiv, Kyiv (Ukraine) 1987–1998 Professor Taras Shevchenko National University of Kyiv, Kyiv (Ukraine) 1998–2003 Head of the Department of Probability Theory and Mathematical Statistics Taras Shevchenko National University of Kyiv, Kyiv (Ukraine) 2003–Present Full Professor Taras Shevchenko National University of Kyiv, Kyiv (Ukraine) EDUCATION AND TRAINING 1963 BSc + MSc Taras Shevchenko National University of Kyiv, Kyiv (Ukraine) 1968 PhD Taras Shevchenko National University of Kiev, Kyiv (Ukraine) 1985 DSc Taras Shevchenko National University of Kiev, Kyiv (Ukraine)

# Stochastic processes and fields with values in functional spaces, simulation of random processes and fields, applied statistics

Research Fields:
Mathematics

## Previous and Current Research

•  Analytical properties of stochastic processes; distribution estimation of functionals from random processes
•  Random processes in Orlicz spaces
•  Pre-Gaussian and sub-Gaussian random processes
•  Cauchy problem for mathematical physics equations with random initial conditions
•  Simulation of random processes
•  Statistics of random processes
•  Wavelet expansions of random processes

Our research is concentrated on the development of approximations for paths of random processes with given accuracy and reliability and estimation of functional of these paths.

The team consists of 10 researchers: 1 DSc, 6 PhD candidates and 3 PhD students. We maintain close collaboration with universities of Rome and Melbourne.

We were the first who investigated convergence of wavelet expansions of Gaussian and phi-sub-Gaussian processes and considered new expansions of random processes in series with uncorrelated or independent values. This enables us not only to simulate a process with given accuracy and reliability, but also to approximate the process by intervals of these series with given accuracy.

Now we study conditions and rate of convergence for wavelet expansions of random processes from Orlicz and other special spaces. We investigate convergence of the Kotelnikov-Shannon approximations in C(T) for Gaussian stationary processes with bounded spectrum and in L_p(T) for processes with unbounded spectrum.

## Future Projects and Goals

• Wavelet expansions of random processes in Orlicz spaces and the Kotelnikov-Shannon approximations
• Simulation of Gaussian, phi-sub-Gaussian and other random fields with given accuracy and reliability in the spaces C(T), C^1(T) and L_p(T)
• Simulation of random processes and fields with stochastic differential equations with fractional operators
• Analytic properties of random fields from special spaces of random variables
• Monte Carlo Methods for calculation of integral functionals
• Analysis of generalized models of random processes connected with differential equations
• Equation of thermal conductivity with random initial conditions and random boundary conditions

## Selected Publications

Kozachenko Y., Olenko A., Polosmak O.
Convergence in $L_p([0,T])$ of wavelet expansions of $\phi$-Sub-Gaussian random processes.
Methodology and Computing in Applied Probability. – 2015. – Vol. 17 (1). – P. 139-153.

Kozachenko Y., Troshki N.V.
Accuracy and reliability of a model of Gaussian random processes in C(T) space.
International Journal of Statistics and Magement System. – 2015. – Vol. 10 (1-2). – P. 1-15.

Kozachenko Y., Troshki V.
A criterion for testing hypotheses about the covariance function of a stationary Gaussian stochastic process.
Modern Stochastics: Theory and Application. – 2014. – Vol. 1 (2). – P. 139-149.

Kozachenko Y.V., Slyvka-Tylyshchak A.I.
The Cauchy problem for the heat equation with a random right side.
Random Operators and Stochastic Equations. – 2014. – Vol. 22 (1). – P. 53-64.

Kozachenko Y., Olenko A., Polosmak O.
Uniform convergence of compactly supported wavelet expansions of Gaussian random processes.
Communications in Statistics - Theory and Methods. – 2014. – Vol. 43 (10-12). – P. 2549-2562.

Yamnenko R., Kozachenko Y., Bushmitch D.
Generalized sub-Gaussian fractional Brownian motion queueing model.
Queueing Systems. – 2014. – Vol. 77 (1). – P. 75-96.

Kozachenko Y., Sergiienko M.
Estimates of distributions for some functionals of stochastic processes from an Orlicz space.
Random Operators and Stochastic Equations. – 2014. – Vol. 22 (2). – P. 65-72.

Kozachenko Y.V., Sergiienko M.P.
The criterion of hypothesis testing on the covariance function of a Gaussian stochastic process.
Monte Carlo Methods and Applications. – 2014. – Vol. 20 (2). – P. 137-144.

Giuliano Antonini R., Hu T.-C., Kozachenko Y., Volodin A.
An application of $\phi$-subgaussian technique to Fourier analysis.
Journal of Mathematical Analysis and Applications. – 2013. – Vol. 408. – P. 114-124.

Kozachenko Y., Olenko A., Polosmak O.
On convergence of general wavelet decompositions of nonstationary stochastic processes.
Electronic Journal of Probability. – 2013. – Vol. 18. – Article 69. – 21 p.

Kozachenko Yu.V., Mlavets′ Yu.Yu.
The Banach spaces $F_{\psi}(Ω)$ of random variables.
Theory of Probability and Mathematical Statistics. – 2013. – Vol. 86. – P. 105-121.

Kozachenko Y., Pashko A.
Accuracy of simulations of the Gaussian random processes with continuous spectrum.
Computer Modeling and New Technologies. – 2014. – Vol. 18 (3). – P. 7-12.

Kozachenko Y., Pogoriliak O.
Simulation of Cox processes driven by random Gaussian field.
Methodology and Computing in Applied Probability. – 2011. – Vol. 13 (3). – P. 511-521.

Kozachenko Yu., Sottinen T., Vasylyk O.
Lipschitz conditions for $Sub_{\phi}(\Omega)$-processes and applications to weakly self-similar processes with stationary increments.
Theory of Probability and Mathematical Statistics. – 2011. – Vol. 82. – P. 57-73.

## Contacts

Homepage: http://probability.univ.kiev.ua/index.php?page=userinfo&person=yvk&lan=en

yvk@univ.kiev.ua