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Department of Probability Theory,

Statistics

and Actuarial Mathematics

Mechanics and Mathematics

faculty

prob.stat.act@gmail.com, probability@univ.kiev.ua

Tel/Fax: +38 (044) 259 03 92

Professor D. Grave (1863 -- 1939) was the first lecturer in actuarial mathematics. He published the textbooks: ``Mathematics of Insurance'' (1912), ``Theory of Pension Funds'' (1917), ``Mathematics of Social Insurance'' (1924). Thus, together with University of Stockholm (F. Lundberg, H. Cramer) Kyiv University was the pioneer in creation and development of actuarial mathematics.

It is worth to recall the eminent scientist Eugene Slutskyi (1880 - 1948), who was a founder of mathematical economics and theory of stochastic processes (together with A. Khinchin and A. Kolmogorov). E. Slutskyi is one of the famous graduates of Kyiv University.

In the late twenties and early thirties of the twentieth century academician Mikhail Kravchuk (1892 - 1942) developed probability-theoretical and statistical research at Kyiv University. M. Kravchuk and his disciples O.Smogorzhevskyi (1896 -- 1969), K.Latysheva (1897 -- 1956), O.Lebedyntseva, S.Kulyk studied orthogonal polynomials corresponding to some probability distributions. Nowadays, polynomials generated by Bernoulli distribution bear Kravchuk's name.

In 1934 Mykola (Nikolai) Bogolyubov (1909 - 1992) started to work at the University. At that time M. Bogolyubov and M. Krylov (1879 - 1955) published their classical papers on ergodic theory of Markov chains with an arbitrary phase space. The paper ``On Fokker-Planck equations derived in the theory of perturbation by the method based on spectral properties of the perturbation Hamiltonian'' played very important role in the development of theory of stochastic processes. Mathematical substantiation of this paper resulted in creation of the theory of stochastic differential equations which is one of the most important parts of modern theory of stochastic processes.

In 1939 - 1941 Bogolyubov's post-graduate student Iosyp Gikhman (1918 - 1985) studied dynamic systems influenced by random forces, striving to substantiate the limit transitions. Just before World War II he had prepared candidate's (Ph.D.) thesis ``Dynamic systems under the influence of random forces''. During the war Gikhman was in the army in the field. In 1942, during a short leave from the army, he defended his Ph.D. thesis at the Institute of Mathematics of Uzbekistan Academy of Sciences. After the war 1945 I. Gikhman worked at the Roads and Vehicle Institute (1945 - 1947) and at Kyiv University (since 1947). He focused on the rigorous definition of stochastic differential equation and conditions for existence of its solutions. Concurrently, K. Ito was studying similar problems far away in Japan.

According to archival documents, in 1945 Mechanics and Mathematics Faculty of Kyiv University consisted of seven departments: mathematical analysis, geometry, algebra and probability theory, elasticity theory, mathematical physics and function theory, engineering mechanics, general mathematics. Department of Algebra and Probability Theory was headed by associated professor M.Sokolov. S.Avramenko, O.Lebedyntseva and I.Gikhman worked at the Department.

In 1949 academician of the Ukrainian Academy of Sciences Borys Gnedenko became a Head of Department of Algebra and Probability Theory at Kyiv University. B. Gnedenko was a disciple of A. Kolmogorov and A. Khinchin and brought to Kyiv University the best traditions and spirit of the Moscow mathematical school. This school featured with the support of aspiration of young mathematicians to carry out independent research and also in the involving of young people in scientific work. No wonder, B. Gnedenko attracted a lot of young scientists. Among his first students were future academicians V. Korolyuk, V. Mykhalevych, A. Skorokhod.

In 1949 the ``Radyanska Shkola'' publishing house issued the first Ukrainian language edition of the textbook ``The Course of Probability Theory'' by B. Gnedenko. One can hardly recall another textbook, which have run through so many editions in several languages: 8 editions in Russian, 11 in German, 6 in English. Also the textbook was translated in Hungarian, Polish, Japanese, Chinese, French, Italian, Vietnamese and Arabic languages.

In 1955, when the Head of Department of Mathematical Analysis G. Shylov moved to Moscow, this department was united with Department of Algebra and Probability Theory into Department of Mathematical Analysis, Probability Theory and Algebra. In 1956 some new scientists joined the department: professor L.Kaluzhnin, senior lecturers V.Mykhalevych and A.Skorokhod. Also, V.Glushkov, O.Parasyuk, V.Koroluuk and K.Yushchenko (Rvachova) worked at the department.

At the beginning of 1958 Borys Gnedenko managed to overcome numerous bureaucratic obstacles and got a permission to create the specialization ``Probability Theory and Mathematical Statistics'' at the Mechanics and Mathematics Faculty of Kyiv University. Students specializing in probability theory attended mandatory courses ``Additional topics on probability theory'', ``Theory of stochastic processes'', ``Mathematical statistics''.

In 1958 Borys Gnedenko stopped his work at Kyiv University, but he always maintained close relations with Department of Probability Theory of Kyiv University. Shortly before his death in 1993 Borys Gnedenko wrote: ``I am happy that destiny committed me with the honourable mission to found probability-theoretical school in Ukraine. Now, a lot of my scientific grandchildren and great-grandchildren have joined this school. It has won a serious position in the life of modern probability theory. It is very important for it to gain not only in quantity, but in quality, to discover new fields of research and to keep in touch with practice''.

After Borys Gnedenko left Kyiv University, Department of Mathematical Analysis and Probability Theory was headed by O. Parasyuk, and then by V. Dzyadyk.

In 1962 the separate Department of Probability Theory and Mathematical Statistics was created and professor I. Gikhman became its head. The teaching staff of the new department consisted of associated professor A.Skorokhod, senior lecturer M.Yadrenko, assistant professors A.Dorogovtsev, M.Slobodenyuk, V.Baklan, I.Ezhov. Number of post-graduate students increased, there were first foreign post-graduate students -- H.Hekendorff (Germany), Li Shi Lin', Gan' Chzhan Zjuan' (Chinese People Republic).

In 1961 Kyiv University Press published A. Skorokhod's monograph ``Research in the Theory of Stochastic Processes'' which became a basis for his doctoral thesis defended in 1963. In 1965 this monograph was translated into English in USA and run through two editions (in 1970, 1982). The monograph imparted a powerful impetus to the development of the theory of stochastic processes in the sixties - nineties. The notions of ``Skorokhod's method of common probability space'', ``Skorokhod's representation'' (of a sequence of sums of independent random variables by values of the Wiener process), ``Skorokhod's topology'' are often used in modern scientific literature.

In 1964 I.Gikhman and A.Skorokhod accomplished their ``Introduction to Theory of Stochastic Processes'' - the first textbook in this field written in Russian. It run through two editions (1965, 1978) and was translated into English, French, Polish, German, Hungarian and Chinese.

It's impossible to overestimate Skorokhod's role in the development of probability theory at Kyiv University. The list of monographs written by him impresses: ``Research in Theory of Stochastic Processes'' (1961), ``Random Processes with Independent Increments'' (1964; revised edition - 1986), ``Theory of Stochastic Processes'' (co-author I. Gikhman; vol.1, 1971; vol.2, 1973; vol.3, 1975), ``Stochastic Differential Equations'' (co-author I.Gikhman; 1968), ``Limit Theorems for Random Walks'' (co-author M. Slobodenjuk, 1970), ``Integration in Hilbert Space'' (1975), ``Controlled Random Processes'' (co-author I.Gikhman, 1977), ``Random Linear Operators'' (1978), ``Consistent Estimates of Parameters of Random Processes'' (co-author I.Ibramkhalilov, 1980), ``Stochastic Differential Equations and their Applications'' (co-author I.Gikhman, 1982), ``Stochastic Equations for Complex Systems'' (1983), ``Asymptotic Methods in the Theory of Stochastic Differential Equations'' (1987). The majority of mentioned monographs was translated in English.

A. Skorokhod had not been abroad until 1983. This circumstance and a vast of monographs signed by this name gave rise to the hypothesis, spread among foreign mathematicians, that ``A. Skorokhod is a pseudonym of a collective of Ukrainian mathematicians studying stochastic processes''.

In 1965 I. Gikhman was elected a Corresponding Member of the Academy of Sciences of Ukraine and moved to Donetsk where he was appointed the head of departments of probability theory, both at the new Institute for Applied Mathematics and Mechanics and at Donetsk University. I. Gikhman had many disciples. Many generations of Kyiv University graduates, mathematicians of different specialities, recall warmly his wonderful lectures in mathematical analysis, probability theory, functional analysis, integral equations, mathematical physics, number theory, as well as his probabilistic and statistical special courses. Under his guidance M.Yadrenko, A.Dorogovtsev, I.Ezhov, H.Hekenforff, V.Baklan, M.Portenko, O.Illyashenko, B.Kucher, Li Shi Lin', H.Mansurov and A.Shatashvili defended their Ph.D. theses.

The subsequent heads of Department of Probability Theory and Mathematical Statistics were: Corresponding Member of National Academy of Sciences of Ukraine Professor Mikhail Yadrenko (January 1966 - December 1998), Professor Yuriy Kozachenko (December 1998 - December 2003). The present (since December 2003) head is Professor Yuliya Mishura.

In different periods the following scientists worked at the Department: A.Dorogovtsev, I.Ezhov, Yu.Ryzhov, V.Baklan, V.Bandura, G.Pryzva, G.Kulinych, Yu.Kozachenko, D.Silvestrov, M.Kartashov, M.Leonenko, O.Ponomarenko, R.Maiboroda, O.Borysenko, M.Moklyachuk, A.Olenko. Also, A.Skorokhod, V.Korolyuk, V.Shurenkov and M.Portenko gave lectures and were scientific advisors for post-graduate students at the Department as part-time employees.

All these years the Department has been intensively working on preparation of textbooks and tutorials. In particular, the following textbooks were published:

- I. Gikhman, A. Skorokhod, M. Yadrenko ``Probability Theory and Mathematical Statistics'' (1979, 1988),

- A. Dorogovtsev, D. Silvestrov, A. Skorokhod, M. Yadrenko ``Selected Problems in Probability Theory'' (1976, 1980; English translation -- 1998),

- A. Skorokhod ``Lectures in Theory of Stochastic Processes'' (1990),

- A.Skorokhod ``Elements of Probability Theory and Theory of Stochastic Processes'' (1975).

The Department has considerably extended the gamut of scientific research. At present, the main trends of investigation are:

- limit theorems of the theory of stochastic processes;

- theory of random fields;

- statistics of random processes and fields;

- Markov processes; semi-Markov processes;

- stochastic differential equations;

- queueing theory and reliability theory;

- Gaussian random processes and their generalizations;

- stochastic analysis;

- actuarial and financial mathematics.

More than 150 post-graduates defended their Ph.D. theses. Many of them defended afterwards doctoral theses. Now they are prominent scientists and lead important scientific divisions (in particular, at Kyiv University).

The Department of Probability Theory and Mathematical Statistics has become one of the leading organizations in development of the theory of random fields. The research in this area was summarized in the monographs

- ``Spectral Theory of Random Fields'' (1980; English translation -- 1983) by M. Yadrenko ,

- ``Statistical Analysis of Random Fields'' (1986) by M. Leonenko and O. Ivanov,

- ``Limit Theorems for Random Fields with Singular Spectrum'' (1999) by M. Leonenko.

The Department of Probability Theory and Mathematical Statistics of Kiev University is a world-wide known center of high level specialists and scientists training in probability theory, theory of stochastic processes, mathematical statistics and applications of these disciplines. For fifty years the Department has been preparing qualified specialists in probability theory and mathematical statistics within the framework of speciality ``Mathematics''.

In 1995 the Department put forward the initiative to prepare mathematically educated statisticians (or mathematicians specializing in statistics). Since 1996/97 academic year the Mechanics and Mathematics Faculty of Kyiv National University trains bachelors, specialists and masters in the speciality ``Statistics'' on the base of Department of Probability Theory and Mathematical Statistics. The educational program is a standard one for the famous universities teaching in statistics. Within the framework of this speciality the following specialization were developed :

actuarial and financial mathematics;

econometrics and mathematical economics;

applied statistics.

During last few years teachers prepared and published numerous textbooks and tutorials for new statistical specializations. Some of them are listed below.

- Borysenko O. Maiboroda R. ``Analytic Methods in Psychology and Sociology'', Kiev University, 1999.

- Borysenko O., Mishura Yu., Radchenko V., Vasylyk O. ``Collected Problems in Financial Mathematics '', Kyiv University, 2005.

- Kartashov M. ``Strong Stable Markov Chains'', VSP, 1996.

- Kartashov M. ``Probability Theory and Mathematical Statistics'', Kyiv: TBiMC, 2004.

- Kozachenko Yu., Pashko A. ``Simulation of Random Processes'', Kyiv University, 1999.

- Buldygin V., Kozachenko Yu. ``Metric Characteristics of Random Variables and Processes'', Kyiv: TBiMC, 1998 (In Russian). English translation: AMS, Providence RI, 2000.

- Kozachenko Yu. ``Lectures in Wavelet Analysis'', Kyiv: TBiMC, 2004.

- Leonenko, M., Mishura, Yu., Parkhomenko, V., Yadrenko, M. `` Probabilistic and Statistical Methods in Econometrics, Actuarial and Financial Mathematics'', Kyiv, 1995.

- Maiboroda R. ``Computational Statistics'', Kyiv University, 2002.

- Maiboroda R. ``Statistical Analysis of Mixtures'', Kyiv University, 2002.

- Moklyachuk M. ``Calculus of Variations. Extremum Problems'', Kyiv: ``Lybid’'', 1994; Kyiv: VPTS ``Ekspress'', 2003; Moskva: R\&C Dynamics, 2005.

- Moklyachuk M. ``Basics of Convex Analysis'', Kyiv: TBiMC, 2004.

- Olenko A., Yadrenko M. ``Discrete Mathematics'', Kyiv University, 1997.

- Olenko A., Zinchenko N. ``Analytical Models and Methods in Social Sciences'', 1998.

- Olenko A., ``Actuarial Mathematics. Problems'', Kyiv University, 2005.

- Parkhomenko V. ``Methods of Sample Surveys'', Kyiv, 2001.

- Ponomarenko O., Ponomarenko V. ``System Methods in Economics, Management and Business'', Kyiv: ``Lybid’'', 1995.

- Ponomarenko O., Perestyuk M., Burym V. ``Foundations of Mathematical Economics'', Kyiv: ``Informtechnika'', 1995.

- Ponomarenko O. ``Modern Analytical Politology'', Kyiv University, 2000.

- Ponomarenko O. ``Foundations of Financial Mathematics and Insurance'', Kyiv: IPC of State Statistics Committee of Ukraine, 2004.

- Ponomarenko O., Perestyuk M., Burym V. ``Modern Economic Analysis. Macroeconomics'', Kyiv: ``Vyshcha Shkola'', 2001.

- Ponomarenko O., Perestyuk M., Burym V. ``Modern Economic Analysis. Microeconomics'', Kyiv: ``Vyshcha Shkola'', 2001.

- Yadrenko M. ``Discrete Mathematics'', Kyiv: Ekspress, 2003.

In last five years the Department received several International Grants for educational projects in the field of statistical education. This afforded an opportunity to organize modern material and technical basis for providing teaching process in speciality ``Statistics'', to create library of scientific and training literature, and to intensify process of preparation and publishing new textbooks and tutorials.

Besides the traditional trends originated by B.Gnedenko, I.Gikhman, V.Korolyuk, A.Skorokhod and M.Yadrenko and listed above the Department develops new ones. In the last decade, a good deal of the research projects at the Department are devoted to the applied investigations in the national economy problems. Since 1980 the professors and fellows of the Department have been elaborating methods, algorithms and program systems for probabilistic and statistical analysis in the following fields:

- meteorological forecast and ecology;

- processing of trajectory and telemetric information in space investigation;

- reliability analysis of technical products;

- stratification of geological layers;

- analysis of psychological data;

- modelling of stochastic fields; processing and transmission of data.

The staff of the Department takes part in the following researches:

- profound statistical analysis of economic and ecological information, data of psychological and sociological investigations;

- elaboration of forecast methods, classification based on modern theoretically probabilistic methods;

- elaboration of probabilistic mathematical models in econometric and sociometric investigations;

- method elaboration of data storing and defense .

The Department of Probability Theory and Mathematical Statistics was a co-organizer of international schools and conferences:

- The Eighth International School on Mathematical and Statistical Methods in Economics, Finance and Insurance (June, 2004, Foros, Ukraine)

- The Seventh International School on Mathematical and Statistical Methods in Economics, Finance and Insurance (September 2003, Laspi, Ukraine)

- International Gnedenko Conference (June 2002, Kyiv, Ukraine)

- The Sixth International School on Applied Statistics, Actuarial and Financial Mathematics (September 2002, Laspi, Ukraine)

- The Fifth International School on Applied Statistics, Actuarial and Financial Mathematics (June 2001, Gurzuf, Ukraine)

- The Fourth International School on Applied Statistics, Actuarial and Financial Mathematics (January 2001, Vasteras, Sweden)

- The Third International School on Applied Statistics, Actuarial and Financial Mathematics (September 2000, Feodosiya, Ukraine)

- The Third Scandinavian--Ukrainian Conference on Probability and Statistics (June 1999, Kyiv, Ukraine)

- The Second International School on Actuarial and Financial Mathematics (June 1999, Kyiv, Ukraine)

- The First International School on Financial Mathematics and Mathematical Economics (September 1998, Kyiv, Ukraine)

- The Second Scandinavian--Ukrainian Conference on Probability and Statistics (1997, Umea, Sweden)

- The First Scandinavian--Ukrainian Conference on Probability and Statistics (1995, Uzhgorod, Ukraine)

- Ukrainian--Hungarian Conference on Probability Theory (1993, Mukacheve, Ukraine)

The Department publishes two journals: the scientific journal ``Theory of Probability and Mathematical Statistics'' and the popular scientific one ``In the World of Mathematics''.

``Theory of Probability and Mathematical Statistics'' was founded in 1970. Two issues appear annually. The editor-in-chief is A. Skorokhod, assistants to the editor-in-chief are Yu. Kozachenko and M. Portenko, the editorial board secretary is A. Olenko. The journal is translated into English and published in the USA by the American Mathematical Society.

Original articles, surveys, and reviews on monographs in probability theory, theory of random processes and fields, mathematical statistics and its applications are published in this journal. This edition is intended for specialists in probability theory , high school teachers, scientific workers, dealing with applications of statistical and probability theory methods, and also for post-graduate students.

``In the World of Mathematics'' is the only scientific popular mathematics journal in Ukraine. It is designed first of all for schoolchildren, but many materials may be useful and interesting also for students, teachers and everyone interested in mathematics. The journal relates about the newest achievements in mathematics, unsolved problems and various applications of mathematics in different spheres of knowledge. The goal of the journal is to develop the readers’ creative abilities, involve them into scientific work, and also to search for gifted pupils. Therefore the journal gives a lot of information about mathematical olympiads, competitions, and creative contests. The members of the editorial board assist in organizing the Ukrainian mathematical Olympiads and selecting the team for international mathematical olympiads. The journal contains a lot of entertaining materials -- mathematical games, mathematical fairy tales and detective stories, puzzles, rebuses. Interesting chess page and news of mathematical life are also presented in the journal.

Besides that, Department takes an active part in the edition of three other scientific journals: ``Theory of Stochastic Processes'', ``Random Operators and Stochastic Equations'' and ``Applied Statistics, Actuarial and Financial Mathematics''.

Training of high level professional specialists, competitive in the labor market, is impossible without the European teaching experience and collaboration with leading educational centers of Europe. Essential help to Ukraine in this area is being rendered by the European Union within the framework of the TEMPUS-TACIS Programme aimed at the development of cooperation between higher education institutions of the European Union and Ukraine.

According to this programme the Department of Probability Theory and Mathematical Statistics participated in the TEMPUS-TACIS JEP - 10353-97 Project ``Statistical Aspects of Economics'' in cooperation with the Universities of Stockholm (Sweden), Umea (Sweden) and Helsinki (Finland) and in the TEMPUS-TACIS Network Project NP-22012 - 2001 ``Improvement of Education in Statistical Applications in Economics'' in cooperation with the Universities of Stockholm (Sweden), Vasteros (Sweden) and Helsinki (Finland).

The creation of the Network of Ukrainian universities and practitioners ``Economic-Statistical Education in Ukraine'' was a key success of the Network Project. The founders of the Network were Kyiv National Taras Shevchenko University, Nizhyn Pedagogical University, Uzhgorod National University and Ukrainian State Committee in Statistics. The great organizational work and successful dissemination actions attracted the non-consortium members and promoted increasing the number of network members: Lviv, Chernivtsi, Volyn (Lutsk), Donetsk, Dnepropetrovsk and Kherson Universities. All new members were involved in the Network activities: curricula/course development, exchange of information, training and dissemination.

Due to realization of the projects the Department of Probability Theory and Mathematical Statistics of Kyiv University has become the center of implementation and dissemination of know-how, modern teaching methodology and good practices in new economic-statistical specialities. These projects are good examples of useful bilateral and multilateral dialogue and cooperation between European and Ukrainian Universities.

Now Department of Probability Theory and Mathematical Statistics is participating in Joint European Project IB-JEP-25054-2004 ``Training Centre for Actuaries and Financial Analysts'', 2005-2008, which is carried out within the framework of TEMPUS Program (Trans-European Cooperation Scheme for Higher Education) financed by European Commission (Directorate-General for Education and Culture).

The Ukrainian participants of the project are:

- State Commission for Regulation of Financial Services Markets of Ukraine (Statefinservices), governmental structure responsible for qualification demands and certification of specialists eligible to fulfil actuarial calculation according to the law ``On Insurance'',

- Kyiv National Taras Shevchenko University (academic institution which will develop and deliver the training courses) and

- Society of Actuaries of Ukraine (SAU), non-state professional association.

- Malardalen University (Sweden),

- Stockholm University (Sweden),

- Catholic University of Leuven (Belgium),

- University of Cologne (Germany),

- University of Aegean (Greece).

The Project Coordinator is Professor Dmitrii Silvestrov (Malardalen University, Vasteras, Sweden).

The strategic goal of this project is to assist in the development of actuarial profession in Ukraine through the implementation of the system of actuaries training. It presents several immediate steps straightforwardly responding demands of insurance/financial sector of economy. The project is aimed at establishing proper professional standards and increasing the role of actuarial profession in Ukraine and therefore developing the strong insurance services industry in Ukraine as an essential element of social protection and civil society development.