Ruslan Stratonovich

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Ruslan Leontyevich Stratonovich
Born (1930-05-31)May 31, 1930
Moscow, Russia (Soviet Union)
Died January 13, 1997(1997-01-13) (aged 66)
Moscow, Russia
Fields Mathematics
Alma mater Moscow State University
Doctoral students Viacheslav Belavkin
Known for Stratonovich integral
Notable awards State Prize of the Russian Federation

Ruslan Leont'evich Stratonovich (Russian: Русла́н Лео́нтьевич Страто́нович) was a Russian physicist, engineer, and probabilist and one of the founders of the theory of stochastic differential equations.


Ruslan Stratonovich was born May 31, 1930 in Moscow. He studied from 1947 at the Moscow State University, specializing in there under P. I. Kuznetsov on radio physics (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. 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 Moscow State University.


Stratonovich invented a stochastic calculus which serves as an alternative to the Itō calculus; the Stratonovich calculus is most natural when physical laws are being considered. The Stratonovich integral appears in his stochastic calculus. 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 processes, which was published in his papers in 1959 and 1960. The Kalman-Bucy (linear) filter (1961) is a special case of Stratonovich's filter. [1]

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). [2][3]

In 1965, he developed the theory of pricing information (Value of information), which describes decision-making situations in which it comes to the question of how much someone is going to pay for information.[4]



  • 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)


  1. Stratonovich first met Kalman in a conference in Moscow in 1960 and corresponded with him from then on
  2. Stratonovich On a Method of Calculating Quantum Distribution Functions, Soviet Physics Doklady, Band 2, 1958, S. 41
  3. Hubbard Calculation of Partition Functions, Physical Review Letters, Band 3, 1959, S. 77
  4. Stratonovich On value of information, Izvestiya of USSR Academy of Sciences, Technical Cybernetics 5, 1965, S. 3–12

Further reading

  • F V Bunkin et al., In memory of Ruslan Leont'evich Stratonovich, Physics-Uspekhi 40, 751-752, 1997 article
  • Professor R.L. Stratonovich: reminiscences of relatives, colleagues and friends edited by Yu. M. Romanovski, Publishing House of Computer Research Institute, Moscow-Izhevsk, 2007, 174 pages (in Russian). ISBN 978-5-93972-606-1. This book contains the full list of Stratonovich's publications (monographs and journal papers, 185 items in total).
  • M. S. Yarlykov, Yu. A. Soloviev To the 80th Birthday of R. L. Stratonovich, Automation and Remote Control, Band 71, 2010, S. 1447-1450, Springer Link