Igor Vladimirovich Girsanov (russian: И́горь Влади́мирович Гирсанов; (10 September 1934 – 16 March 1967) was a Russian

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, structure, space, models, and change. History On ...

. He made major contributions to

probability theory Probability theory 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 expressing it through a set o ...

and its applications.

Early life

Igor Girsanov was born on 10 September 1934, in

Turkestan Turkestan, also spelled Turkistan ( fa, ترکستان, Torkestân, lit=Land of the Turks), is a historical region in Central Asia corresponding to the regions of Transoxiana and Xinjiang. Overview Known as Turan to the Persians, western Turke ...

(then

Kazakh ASSR The Kazakh Autonomous Socialist Soviet Republic (russian: Казахская Автономная Социалистическая Советская Республика; kk, Qazaq Aptonom Sotsijalistik Sovettik Respublikasь), abbreviated as K ...

). He studied in

Baku Baku (, ; az, Bakı ) is the capital and largest city of Azerbaijan, as well as the largest city on the Caspian Sea and of the Caucasus region. Baku is located below sea level, which makes it the lowest lying national capital in the world a ...

until his family moved to

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

in 1950. While at school he was an active member of the Moscow State University maths club and won multiple Moscow mathematics olympiads.

Education

Between 1952 and 1960 Girsanov was an undergraduate and graduate student at Moscow State University. After his graduation he joined the faculty. In 1965 he became Head of the newly formed Probability and Statistics Laboratory at MSU.

Academic work

One can distinguish two periods in Girsanov's academic work. Prior to 1961, he worked as a member of a group of mathematicians united around E. B. Dynkin who were developing the theory of

Markov process A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...

es. His thesis introduced the concept of a strong

Feller process In probability theory relating to stochastic processes, a Feller process is a particular kind of Markov process. Definitions Let ''X'' be a locally compact Hausdorff space with a countable base. Let ''C''0(''X'') denote the space of all rea ...

which proved to be particularly useful. In the same thesis he considered the problem of applying Markov processes to the solution of

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s. He was among the first scientists to study elliptic and parabolic equations with discontinuous coefficients. In his papers on stochastic differential equations he determined the conditions when the discontinuity of the coefficients does not prevent the solution from being unique. He also produced important papers on the general theory of Markov processes. Girsanov was able to learn areas of mathematics that were unfamiliar to him very quickly. At the same time he was considering questions unrelated to stochastic processes. For example, he constructed an example of a

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...

with a simple spectrum. In collaboration with B. S. Mityagin he worked on

quasi-invariant measure In mathematics, a quasi-invariant measure ''μ'' with respect to a transformation ''T'', from a measure space ''X'' to itself, is a measure which, roughly speaking, is multiplied by a numerical function of ''T''. An important class of examples occ ...

s on topological

linear space In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', may be added together and multiplied ("scaled") by numbers called '' scalars''. Scalars are often real numbers, but can ...

s. Around 1960 the problems of optimal management in industry and economics came to the fore in USSR. Many mathematicians were working in this area, mostly using familiar mathematical tools. Girsanov also started to work within this framework. But in 1961 he changed his approach. He began to develop a broader understanding of the issues at hand, developing new mathematical techniques. Girsanov became an advocate of

mathematical economics Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference an ...

, actively defending it against the opponents of quantitative methods. His research results had applications in industry. He published fifteen papers on applications to chemistry. His interests included the

optimal control Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and ...

of chemical reactors. He also maintained his interest in theoretical mathematics developing the

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

required for optimisation problems.

Death

Girsanov died on 16 March 1967 at the age of 32 as a result of an accident during a hike in the

Sayan Mountains The Sayan Mountains (russian: Саяны ''Sajany''; mn, Соёны нуруу, ''Soyonï nurû''; otk, 𐰚𐰇𐰏𐰢𐰤, Kögmen) are a mountain range in southern Siberia, Russia (Buryatia, Irkutsk Oblast, Krasnoyarsk Krai, Tuva Republic ...

References

1934 births 1967 deaths 20th-century Russian mathematicians {{russia-mathematician-stub