Jevgenijs CARKOVS

Professor Jevgenijs CARKOVS (Ye. TSARKOV) Professor of Probability Theory and Mathematical Statistics Specialized Institute of Mathematical Statistics, Faculty of Computer Science an Information Technology, Riga Technical University Meza iela 1/4, 438 Riga, LV 1048 Latvia Phone: +371 708 9517 Fax: +371 782 0094 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 of Securities
• Dynamical Systems

Languages: Russian, Latvian, Ukrainian, English

Education

• Chernovtsy State University (Faculty of Physics and Mathematics), Ukraine, 1959
• Dr.math. (Candidate of Science in former USSR, Ph.D. in Western countries), University of Latvia, 1966
• Dr.habil.math. (Doctor of Science in former USSR), Mathematical Institute of Ukraine, Kiev, 1983

Experienc:

• 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 and Director, Specialized Institute of Mathematical Statistics, Faculty of Computer Science and Computer Engineering, Riga Technical University, 1995 -
• Professor, Faculty of Physics and Mathematics, University of Latvia, 1984
• Visiting Scholar and Professor at:

- Science & Technology University of Hong Kong (Hong Kong), 1995, 1996
- 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

• 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 Courses

Riga Technical University and University of Latvia:

• Probability Theory and Mathematical Statistics
• Funkcional Analysis
• Differential Equations
• Stochastic Processes
• Markov Processes
• Testing Statistical Hypotheses
• Stochastic Analysis of Securities Market

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 Inernational Workshop on Statistical Modelling (Eds.: Verboke,G., Molenberghs,G., Aerts,A., and Fieuws,S.) Leuven: Katholieke Universiteit 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.

Research Projects:

• J.Carkovs (Head of Project). Limit Theorems for Stochastic Dynamical Systems. Latvian Council of Science (1994-1996).
• J.Carkovs (Head of Project). Asymptotical Methods for Stochastic Dynamics. Latvian Council of Science (1997-1999).
• J.Carkovs (Head of Project). Asymptotic Methods of  Stochastic Analysis. Latvian Council of Science (2001 - 2004).
• J.Carkovs (Head of Project). Asymptotic Analysis of  StochasticStability . Latvian Council of Science (2005 - ).

Last update 26.02.2007