Myhailo Yosypovych Yadrenko () was born April 16, 1932, in the village of Drimailivka ( Kulykivka district,

Chernihiv Chernihiv (, ; , ) is a city and municipality in northern Ukraine, which serves as the administrative center of Chernihiv Oblast and Chernihiv Raion within the oblast. Chernihiv's population is The city was designated as a Hero City of Ukraine ...

region,

Ukraine Ukraine is a country in Eastern Europe. It is the List of European countries by area, second-largest country in Europe after Russia, which Russia–Ukraine border, borders it to the east and northeast. Ukraine also borders Belarus to the nor ...

) and died September 28, 2004, in

Kyiv Kyiv, also Kiev, is the capital and most populous List of cities in Ukraine, city of Ukraine. Located in the north-central part of the country, it straddles both sides of the Dnieper, Dnieper River. As of 1 January 2022, its population was 2, ...

. Yadrenko was a prominent Ukrainian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

pedagogue Pedagogy (), most commonly understood as the approach to teaching, is the theory and practice of learning, and how this process influences, and is influenced by, the social, political, and psychological development of learners. Pedagogy, taken ...

, Corresponding Member of the Ukrainian National Academy of Sciences, and head of the Department of

Probability Theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...

and

Mathematical Statistics Mathematical statistics is the application of probability theory and other mathematical concepts to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques that are commonly used in statistics inc ...

at Kiev State University of Ukraine.

Life and scientific activity

From 1950 to 1955, Yadrenko was a student at the Department of

Mechanics Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...

and

Mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

at the Kiev University, where he attended lectures of prominent mathematicians and teachers such as N.N. Bogolyubov, B.V. Gnedenko, and I.I. Gikhman. Under their guidance, Yadrenko began his scientific studies and published his first scientific work devoted to the investigation of properties of

random walk In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some Space (mathematics), mathematical space. An elementary example of a rand ...

s. From 1955 to 1958, he was a

postgraduate student Postgraduate education, graduate education, or graduate school consists of academic or professional degrees, certificates, diplomas, or other qualifications usually pursued by post-secondary students who have earned an undergraduate (bachelor' ...

at the Kiev University. In those years, Yadrenko began his studies of

homogeneous Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, i ...

and

isotropic In physics and geometry, isotropy () is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence '' anisotropy''. ''Anisotropy'' is also ...

random field In physics and mathematics, a random field is a random function over an arbitrary domain (usually a multi-dimensional space such as \mathbb^n). That is, it is a function f(x) that takes on a random value at each point x \in \mathbb^n(or some other ...

s. These investigations were presented in his candidate-degree thesis. After postgraduate courses, Yadrenko worked at the Department of

Mathematical Analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...

and Probability Theory at the Kiev University. He devoted much energy to the development of

mathematical education In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge. Although r ...

secondary schools A secondary school, high school, or senior school, is an institution that provides secondary education. Some secondary schools provide both ''lower secondary education'' (ages 11 to 14) and ''upper secondary education'' (ages 14 to 18), i.e., b ...

, organization of mathematical competitions, and publication of contemporary

textbook A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions, but also of learners ( ...

s on

elementary mathematics Elementary mathematics, also known as primary or secondary school mathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical c ...

and

combinatorial analysis Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ap ...

and books of problems of mathematical competitions. In 1966, Yadrenko became the head of the Department of Probability Theory and Mathematical Statistics, a position he held for more than 32 years. Under his guidance, the researchers of the department carried out research in the

spectral theory In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operator (mathematics), operators in a variety of mathematical ...

of random fields (in particular, his doctoral-degree thesis, which is a

Soviet doctorate The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a transcontinental country that spanned much of Eurasia from 1922 until it dissolved in 1991. During its existence, it was the largest country by area ...

, was devoted to this theory),

asymptotic In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the ''x'' or ''y'' coordinates Limit of a function#Limits at infinity, tends to infinity. In pro ...

methods in probability theory, the theory of

stochastic differential equation A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics an ...

s, and applied problems in probability theory and mathematical statistics. The Department of Probability Theory and Mathematical Statistics was repeatedly distinguished as the best department of Kiev University. In 1970, the ''Probability Theory and Mathematical Statistics'' journal () was founded on Yadrenko's initiative. This journal has played an important role in the development of the world-renowned Kiev school of probability theory. Since 1974, the journal is translated into English and is republished by the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. In 1969, Yadrenko founded another periodical edition, a collection of popular-science articles ''In the World of Mathematics'' (). In 1995, this periodical collection was transformed into a popular

scientific Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...

methodological In its most common sense, methodology is the study of research methods. However, the term can also refer to the methods themselves or to the philosophical discussion of associated background assumptions. A method is a structured procedure for bri ...

, and

historical History is the systematic study of the past, focusing primarily on the human past. As an academic discipline, it analyses and interprets evidence to construct narratives about what happened and explain why it happened. Some theorists categ ...

journal. This journal is intended for a broad circle of readers interested in mathematics from schoolchildren to professional mathematicians. As a scientist, Yadrenko is known for his works on the theory of random fields and their

statistical analysis Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of ...

. He wrote more than 200 articles in this field, the majority of which were translated into English. A survey of the results obtained by Yadrenko in the theory of random fields can be found in the paper "On Yadrenko’s works in the theory of random fields". Yadrenko's monograph "Spectral Theory of Random Fields" became a handbook for experts in random fields. This book was awarded the Prize of Ukrainian Ministry of Education, and its English version was published in 1983 in the United States. Yadrenko developed the spectral theory of homogeneous and

random fields in Euclidean,

Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosophy of mathematics, philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad ...

, and Lobachevskii spaces. These results were used by Yadrenko and his

disciple A disciple is a follower and student of a mentor, teacher, or other figure. It can refer to: Religion * Disciple (Christianity), a student of Jesus Christ * Twelve Apostles of Jesus, sometimes called the Twelve Disciples * Seventy disciples in t ...

s for the solution of important problems of linear

prediction A prediction (Latin ''præ-'', "before," and ''dictum'', "something said") or forecast is a statement about a future event or about future data. Predictions are often, but not always, based upon experience or knowledge of forecasters. There ...

and

filtration Filtration is a physical separation process that separates solid matter and fluid from a mixture using a ''filter medium'' that has a complex structure through which only the fluid can pass. Solid particles that cannot pass through the filte ...

of random fields. He founded the theory of

Markov Markov ( Bulgarian, ), Markova, and Markoff are common surnames used in Russia and Bulgaria. Notable people with the name include: Academics * Ivana Markova (1938–2024), Czechoslovak-British emeritus professor of psychology at the University of S ...

random fields, which represented a new direction in the theory of random fields. Later, the theory of

Markov random field In the domain of physics and probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph In discrete mathematics, particularly ...

s was further developed in works related to problems of

statistical physics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...

and

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...

. Yadrenko studied the analytic properties of

choice function Let ''X'' be a set of sets none of which are empty. Then a choice function (selector, selection) on ''X'' is a mathematical function ''f'' that is defined on ''X'' such that ''f'' is a mapping that assigns each element of ''X'' to one of its ele ...

s of random fields. In particular, he established conditions for the continuity, analyticity, and quasianalyticity of random fields. Yadrenko also investigated problems of statistics of random fields. For example, he established conditions for the

absolute continuity In calculus and real analysis, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity. The notion of absolute continuity allows one to obtain generalizations of the relationship between ...

and singularity of measures that correspond to

Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...

ian random fields, and he developed efficient methods for the solution of statistical problems for random fields (problems of

extrapolation In mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. ...

, filtration,

interpolation In the mathematics, mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one ...

, and

estimation Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is d ...

regression coefficient In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A model with exactly one explanatory variable ...

s). Yadrenko worked in various branches of applied probability theory, including optimal methods for quality control in mass production, statistical modeling of noises in

semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...

s, statistical analysis of

random number generator Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that cannot be reasonably predicted better than by random chance. This means that the particular ou ...

s, statistical problems of

reliability theory Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability is defined as the probability that a product, system, or service will perform its intended funct ...

, and statistical models of

distributions Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a varia ...

with random intensity. For a series of works in the theory of random fields, Yadrenko was awarded the Krylov Prize of the Ukrainian National Academy of Sciences. Yadrenko was the founder and the leader of a scientific school in random fields and stochastic processes. Among his disciples, there are 45 candidates of science. Ten of his disciples became doctors of sciences (Soviet doctorate): V.V. Anisimov (Corresponding Member of the Ukrainian National Academy of Sciences) and professors V. L. Girko, Yu. V. Kozachenko, O. I. Klesov, M. M. Leonenko, Yu. D. Popov, D. S. Sil'vestrov, N. M. Zinchenko, M. P. Moklyachuk, and A.B. Kachyns'kyi. Yadrenko was a skilled teacher. His lectures were characterized by mathematical rigorousness, high scientific level, and clarity of presentation. Many Ukrainian experts in probability theory and mathematical statistics learned these branches of mathematics at his lectures. Yadrenko was the author of 24 textbooks on different branches of mathematics, including ''Probability Theory and Mathematical Statistics'' ()''Probability Theory and Mathematical Statistics'', (Yadrenko, I. I. Gikhman and A. V. Skorokhod) Vyshcha Shkola, Kiev (1988) and an unparalleled book of problems in probability theory (written together with A. V. Skorokhod, A. Ya. Dorogovtsev, and D. S. Sil’vestrov), the English version of which was published in 1997 in the United States. In 1995, for the first time in Ukraine, Yadrenko began to deliver lectures on

actuarial mathematics Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, pension, finance, investment and other industries and professions. Actuaries are professionals trained in this discipline. In ma ...

and the theory of insurance risk. Together with his disciples M. M. Leonenko, Yu. S. Mishura, and V. M. Parkhomenko, Yadrenko published the first Ukrainian textbook on

econometrics Econometrics is an application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics", '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8 ...

and contemporary

financial Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Admin ...

and

. Yadrenko is one of the initiators of the introduction of the new mathematical study program "Statistics" in Ukraine. From 1997 to 2001, he headed the Statistical Aspects of Economics global international project within the framework of the TEMPUS-TACIS program of the

European Community The European Economic Community (EEC) was a regional organisation created by the Treaty of Rome of 1957,Today the largely rewritten treaty continues in force as the ''Treaty on the functioning of the European Union'', as renamed by the Lisbo ...

. He also made tremendous contributions to the training of talented young mathematicians. For more than 40 years, he was an organizer of mathematical circles for scholars and school mathematical competitions at different levels. Since 1970, Yadrenko headed the jury of All-Ukrainian mathematical competitions for schoolchildren and students. He also headed the All-Ukrainian correspondence competitions in physics and mathematics, and for many years he delivered TV lectures on mathematics for schoolchildren. In addition, Yadrenko was the Vice-President of the Ukrainian Mathematical Society, a member of the bureau of the Department of Mathematics at the Ukrainian National Academy of Sciences, the Editor-in-Chief of the ''Applied Statistics Actuarial and Financial Mathematics'' () scientific journal, a deputy editor of the ''Theory of Probability and Mathematical Statistics'' () journal, and a member of the Editorial Board of the ''Random Operators and Stochastic Equations'' international journal. For his scientific and pedagogical activities, Yadrenko was awarded numerous medals. In particular, he was awarded the State Prize of Ukraine (2004).

References

External links

Professor Yadrenko's scientific school
{{DEFAULTSORT:Yadrenko, Myhailo 1932 births 2004 deaths 20th-century Ukrainian mathematicians 21st-century Ukrainian mathematicians Taras Shevchenko National University of Kyiv alumni Soviet mathematicians Probability theorists Laureates of the State Prize of Ukraine in Science and Technology People from Chernihiv Oblast Corresponding members of the National Academy of Sciences of Ukraine