Ruslan Leont'evich Stratonovich (russian: Русла́н Лео́нтьевич Страто́нович) was a Russian

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate caus ...

engineer Engineers, as practitioners of engineering, are professionals who invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the l ...

, and probabilist and one of the founders of 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 are used to model various phenomena such as stock p ...

Biography

Ruslan Stratonovich was born May 31, 1930, in

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 ...

. He studied from 1947 at the

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

, specializing in there under P. I. Kuznetsov on

radio physics Radiophysics (also modern writing "radio physics") is a branch of physics focused on the theoretical and experimental study of certain kinds of radiation, its emission, propagation and interaction with matter. The term is used in the following maj ...

(a Soviet term for oscillation physics - including noise - in the broadest sense, but especially in the electromagnetic spectrum). In 1953 he graduated and came into contact with the mathematician

Andrey Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...

. In 1956 he received his doctorate (theory of correlated random points apply to the calculation of electronic noise). In 1969 he became professor of physics at the

Research

Stratonovich invented a

stochastic calculus Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. This field was created an ...

which serves as an alternative to the

Itō calculus Itō may refer to: *Itō (surname), a Japanese surname *Itō, Shizuoka, Shizuoka Prefecture, Japan *Ito District, Wakayama Prefecture, Japan See also * Itô's lemma, used in stochastic calculus *Itoh–Tsujii inversion algorithm, in field theory ...

; the Stratonovich calculus is most natural when physical laws are being considered. The

Stratonovich integral In stochastic processes, the Stratonovich integral (developed simultaneously by Ruslan Stratonovich and Donald Fisk) is a stochastic integral, the most common alternative to the Itô integral. Although the Itô integral is the usual choice in a ...

appears in his

. Here, the Stratonovich integral is named after him (at the same time developed by Donald Fisk). He also solved the problem of optimal non-linear filtering based on his theory of conditional

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, which was published in his papers in 1959 and 1960. The Kalman-Bucy (linear) filter (1961) is a special case of Stratonovich's filter. The Hubbard-Stratonovich transformation in the theory of path integrals (or distribution functions of statistical mechanics) was introduced by him (and used by John Hubbard in solid state physics). In 1965, he developed the theory of pricing information (

Value of information Value of information (VOI or VoI) is the amount a decision maker would be willing to pay for information prior to making a decision. Similar terms VoI is sometimes distinguished into value of perfect information, also called value of clairvoyance ( ...

), which describes decision-making situations in which it comes to the question of how much someone is going to pay for information.R. L. Stratonovich, On value of information, Izvestiya of USSR Academy of Sciences, Technical Cybernetics 5, 3-12 (1965)

Awards

* Lomonosov Prize of the Moscow University, 1984 *

USSR State Prize The USSR State Prize (russian: links=no, Государственная премия СССР, Gosudarstvennaya premiya SSSR) was the Soviet Union's state honor. It was established on 9 September 1966. After the dissolution of the Soviet Union, t ...

, 1988 *

State Prize of the Russian Federation The State Prize of the Russian Federation, officially translated in Russia as Russian Federation National Award, is a state honorary prize established in 1992 following the breakup of the Soviet Union. In 2004 the rules for selection of laureates ...

, 1996

Works

*with P. I. Kuznetsov: The propagation of electromagnetic waves in multiconductor transmission lines, Pergamon Press 1964 *Topics in the theory of random noise, 2 Volumes, Gordon and Breach, 1963, 1967 *with P. I. Kuznetsov, V. I. Tikhonov: Nonlinear transformation of stochastic processes, Pergamon Press 1965 *Conditional Markov processes and their application to the theory of optimal control, Elsevier 1968 *Nonlinear Nonequilibrium Thermodynamics, 2 Volumes, Springer Series in Synergetics, 1992, 1994 (Volume 1: Linear and Nonlinear Fluctuation-Dissipation Theorem, Volume 2: Advanced Theory)

Biography

Research

Awards

See also

Works

References

Further reading