Jevgenijs CARKOVS

Professor Jevgenijs CARKOVS (Ye. TSARKOV) Probability Theory and Mathematical Statistics Chair, Faculty of Computer Science and Computer Engineering, Riga Technical University Meza iela 1/4, 438 Riga, LV 1048 Latvia Phone: +371 6708 9517 Fax: +371 6708 9580 E-mail: carkovs@latnet.lv

Born: December 8, 1935, Rostov-on-Don, Russia

Interests:

• Probability Theory
• Mathematical Statistics
• Stochastic Differential Equations
• Markov Dynamical Systems
• Stochastic Analysis
• Dynamical Systems

Languages: Russian, Latvian, Ukrainian, English

Education

• Chernovtsy State University (Faculty of Physics and Mathematics), Ukraine, 1959

Degrees and Ranks

• Doctor of Science in Physics and Mathematics (Former USSR diploma), 1983
• Professor (Former USSR certificate), 1983
• Dr.habil.math. (LCS diploma), 1992
• RTU professor (RTU diploma), 2000
• Honorary doctor of Chernovtsy University (Ukraine), 2005

Experience:

• Researcher, Senior Researcher, Scientific Secretary, Computing Centre, University of Latvia, 1962-1968
• Associate Professor, Chernovtsy State University, Ukraine, 1968-1972
• Head of Laboratory, Computing Centre, University of Latvia, 1972-1979
• Head of Chair, Riga Technical University, 1979-1995
• Professor of Probability Theory and Mathematical  Statistics, Faculty of Computer Science and Computer Engineering, Riga Technical University, 1984 -
• Principal researcher, Environment Modelling Centre, Faculty of Computer Science and Computer Engineering, Riga Technical University, 2007 -

Visiting Researcher and Professor:

- Hong Kong University of Science & Technology   (Hong Kong), 1995, 1996, 1997
- Michigan State University (East Lansing, USA), 1996
- California Institute of Technology (Los Angeles, USA), 1996
- Linkoeping University (Sweden), 1994, 1995
- Bremen University (Germany), 1993
- Nish University and Belgrade University (Yugoslavia), 1989.

Professional Activities and Memberships

• Supervisor of 31 PhD thesis
• Elected Member, International Statistical Institute, 1993
• Member, American Mathematical Society, 1991
• Member, Kiev Mathematical Society, Ukraine, 1990
• Member, Latvian Mathematical Society, 1993
• Member, Editorial Board for International Journal Random Operators and Stochastic Equations, 1996

Main Teaching Courses

Riga Technical University and University of Latvia:

• Probability Theory and Mathematical Statistics
• Functional Analysis
• Differential Equations
• Stochastic Processes
• Markov Processes
• Testing Statistical Hypotheses
• Stochastic Analysis

Recent/Representative Publications

• J.Carkov. Random Perturbations of Functional Differential Equations, 1986, Riga: Zinatne, 421 p. (in Russian).
• Ye.Tsarkov. Averaging and stability of cocycles under dynamical systems with rapid Markov switching. - Exploring Stochastic Laws, VSP, Utrecht, The Netherlands, 1995, pp.469-479.
• L.Katafygiotis, Ye.Tsarkov. On stability of linear stochastic differential equations. - Random Operators and Stochastic Equations, 1995, vol.3, N 4, pp.352-365.
• M.Sverdan, Ye.Tsarkov. Special finite-difference approximations of flow equations in terms of stream function vorticity and velocity components for viscous incompressible liquid in curvilinear orthogonal coordinates. - Comment. Math. Univ. Carolinae, 1993, vol.34, N 2, pp.165-174
• L.Katafygiotis, Ye.Tsarkov. Mean-square stability of linear dynamical systems with small Markov perturbation. I. Bounded coefficients. - Random Operators and Stochastic Equations, 1996, vol.4, N 2, pp.133-154.
• L.Katafygiotis, Ye.Tsarkov. Mean-square stability of linear dynamical systems with small Markov perturbation. II. Diffusion coefficients. - Random Operators and Stochastic Equations, 1996, vol.4, N 3, pp.257-278.
• L.Katafygiotis, Ye.Tsarkov. Mean-square stability of linear dynamical systems with small Markov perturbation. III. Markov impulse perturbations. - Random Operators and Stochastic Equations, 1996, vol.4, N 4, pp.378-400.
• K.Shadurskis, Ye.F.Tsarkov. On diffusion approximation and stochastic stability. - Theory of Stochastic Processes, 1996, vol.18, N 2, pp.81-95.
• L.Katafygiotis, C.Papadimitriou, Ye.Tsarkov. Mean-square stability of linear stochastic dynamical systems under parametric wide-band excitations. - Probabilistic Engineering Mechanics, 1997, vol.12, N 3, pp.137-147.
• L.Katafygiotis, C.Papadimitriou, Y.Tsarkov. Mean-square stability of linear systems with small bounded stochastic perturbations of their coefficients. - Mechanics Research Communications, 1997, vol.24, N 3, pp.231-236.
• L.Katafygiotis, Ye.Tsarkov. Averaging and stability of qasilinear functial differential equations with Markov parameters. - J. Applied Mathematics and Stochastic Analysis, 1999, vol.12, N 1, pp.1-15.
• Ye.Tsarkov. Asymptotic methods for stability analysis of Markov impulse dynamic systems. - Nonlinear Dynamics and  System Theory, 2002, vol. 2, N 1, pp. 103-115.
• J.Carkovs, K.Sadurskis. On price stochastic equilibrium at randomly delayed supply. - Proc. 1st  Int. Conf. APLIMAT'2002, Slovak University of Technology, Bratislava, Slovakia, 2002, pp. 114-120.
• J.Carkovs, R.Pocs. On price stochastic equilibrium. – Proc. 18th International Workshop on Statistical Modelling (Eds.: Verboke,G., Molenberghs,G., Aerts,A., and Fieuws,S.) Leuven: Katholieke Universities Leuven, 2003, pp.153 – 156.
• J.Carkovs, S.Rogols. Asymptotic methods for stability analysis of linear systems with diffusion coefficients.- Proc. Int. Carphatian Controle Conf. ICCC’2004,University of Science and Technology, Krakow, Poland, 2004, pp. 49-52.
• J.Carkovs. Equilibrium stability of Markov dynamical systems. – Proc. 3^rd Int. Conf. APLIMAT’2004, Slovak University of Technology, Bratislava, Slovakia, 2004, pp.69-82.
• J.Carkovs, K.Sadurskis. Mean square stability of linear systems with Markov coefficients. – Proc. 4^th Int. Conf. APLIMAT’2005, Slovak University of Technology, Bratislava, Slovakia, 2005, pp. 85 – 97.
• J.Carkovs, K.Sadurskis. Averaging method for retarding quasilinear dynamical systems with rapidly oscillating perturbations. – Proceedings of the Latvian Academy of Sciences, 2005, vol.59, Nr 6, pp.245-254.
• J.Carkovs, J.Stoyanov. Asymptotic methods for stability analysis of Markov dynamical systems with fast variables. – In: From Stochastic Analysis to Mathematical Finance. Festschrift for Professor Albert Shiryaev. Kabanov, Yu. and Liptser, R. (Eds.) Springer-Verlag, Berlin, 2005, pp. 93-110.
• J.Carkovs, V.Jasinsky. Asymptotic methods for stability analysis of linear systems with diffusion coefficients. – Theory of Stochastic Processes, 2005, 11(27), Nr. 1-2, pp. 12-23.
• J.Carkovs, V.Korolyuk. On stochastic stability of Markov evolution associated with impulse Markov dynamic systems. – Probability Theory and Mathematical Statistics, 2006, Nr. 75, pp. 60-63.
• J.Carkovs, K.Šadurskis. On delayed stochastic exponent.Proc. of 6^th International Conference APLIMAT’2007 – Slovak University of Technology, Bratislava, Slovakia, 2007, pp. 463 – 469.
• J.Carkovs. On Diffusion Approximation of Discrete Markov Dynamical Systems.Proceedings of World Academy of Science, Engineering and Technology,Volume 30, July, 2008, pp.1-6.
• J.Carkovs, V.Bereza. The construction of Lyapunov-Krasovsky quadratic functional for neutral stochastic differential equations.Proceedings of 7^th International Conference „APLIMAT 2008” Eds. Monika Kovaceva), ISBN: 978-80-89313-03-7. – Slovak University of Technology, Bratislava, Slovakia, pp.179-186.
• J.Carkovs, K.Šadurskis. Exponential stability of fast oscillating linear functional differential equations . Journal of Applied Mathematics, v.1(2008), Nr.1. Slovak University of Technology, Bratislava, Slovakia, pp. 133-139.
• J.Carkovs, A. Egle.On continuous stochastic modelling of heteroskedastic conditional variance Journal of Applied Mathematics.v.2(2009), Nr.2. Slovak University of Technology, Bratislava, Slovakia, pp. 29-42.
• J.Carkovs, V. K. Yasinsky and I. V. Malyk. Stability in impulsive systems with Markov perturbations in averaging scheme. I. Averaging principle for impulsive Markov systems. Cybernetics, Vol. 46, No. 6, 2010, pp. 975-985.
• J.Carkovs, V.K. Yasinsky, and I.V.Malyk. Stability in impulsive systems with Markov perturbations in averaging scheme. 3. Weak convergence of solutions. Cybernetics and Systems Analysis: Volume 47, Issue 3 (2011), pp.442-458.
• J.Carkovs. Time asymptotic of delayed stochastic exponent. In book "Exploring the world of financial engineering". (Ed. A. Malyarenko and Kalev Pärna),Mälardalen University (Sweden), Nordplus Framework project HE-2010_1a-21005, pp.5 - 32.
• J.Carkovs. On delayed geometric Brownian motion. Proceedings of International Conference ASMDA 2011,Roma, June 6-10, 2011, pp.237 - 244.

Research Projects:

• Head of Project. Limit Theorems for Stochastic Dynamical Systems.Latvian Council of Science (1994-1996).
• Head of Project. Asymptotical Methods for Stochastic Dynamics. Latvian Council of Science (1997-1999).
• Head of Project. Asymptotic Methods of  Stochastic Analysis. Latvian Council of Science(2001 - 2004).
• Head of Project. Asymptotic Analysis of  Stochastic Stability. Latvian Council of Science (2005 - 2008).
• Principal executive of Project. Contemporary Methods for  Analysis of Dynamical Systems. (Head of Project F.Sadirbajevs).Latvian Council of Science (2005 - 2008).

Last update 27.07.2012