Grigori Milstein

Professor
Grigori N. Milstein
Professor Grigori N. Milstein
	Grigori Milstein 1998
Born	June 6, 1937; Vinnytsia Oblast, USSR
Died	November 22, 2023 (aged 86); New York[disambiguation needed], United States
Nationality	Russian
Website	michaelvtretyakov.github.io/main/GNMilstein.htm

Grigori N. Milstein (Russian: Григорий Нойхович Мильштейн; 6 June 1937 – 22 November 2023) was a Russian mathematician who made many important contributions to Stochastic Numerics, Estimation, Control, Stability theory, Financial Mathematics.

Biography

G.N. Milstein received his undergraduate degree in mathematics from the Ural State University (UrGU; Sverdlovsk, USSR), which is now Ural Federal University (Ekaterinburg, Russia). He completed his PhD studies at the same university. Milstein has been an assistant professor, associate professor and, after defending his DSc thesis, professor at the Faculty of Mathematics and Mechanics UrGU (then URFU). He also worked as senior researcher at the Weierstrass Institute for Applied Analysis and Stochastics (Berlin, Germany) and was a visiting professor at University of Leicester (Leicester, UK) and University of Manchester (Manchester, UK).

Research

Milstein was a world-leading expert in Stochastic Numerics, Estimation, Control, Stability, Financial Mathematics.

He has published four research monographs: ^[1] ^[2] ^[3] ^[4] The first of the listed books was the first monograph in the world published on the topic of numerical methods for stochastic differential equations. He also contributed to the second edition of R. Khasminskii "Stochastic Stability of Differential Equations", Springer, 2012.^[5]

He has published more than 100 journal papers.

In Milstein's early pioneering papers on Stochastic Numerics (1974,1975),^[6] ^[7] he constructed a first-order mean-square method for SDEs that is known as Milstein method. In 1978, Milstein introduced weak-sense approximations of SDEs for the first time and proposed a number of weak schemes.^[8]

These papers became classics and now are the basis of the modern theory of numerical integration of SDEs. In the 1974 paper Professor Milstein constructed a first-order mean-square method for SDEs that is known as Milstein method. In the 1978 paper Milstein introduced weak-sense approximations of SDEs for the first time and proposed a number of weak schemes.

In 1985-1987 Professor Milstein proved fundamental convergence theorems in the mean-square and weak sense, respectively, which became the foundation for constructing and analysing numerical methods for SDEs.^[9]^[10]

References

^ Milstein, G. N. (1988). Numerical Integration of Stochastic Differential Equations (in Russian). Ural. State Univ., Sverdlovsk.
^ Milstein, G. N. (1995). Numerical Integration of Stochastic Differential Equations. Kluwer Academic Publishers. doi:10.1007/978-94-015-8455-5.
^ Milstein, G. N.; Tretyakov, M. V. (2004). Stochastic Numerics for Mathematical Physics. Springer. doi:10.1007/978-3-662-10063-9.
^ Milstein, G. N.; Tretyakov, M. V. (2021). Stochastic Numerics for Mathematical Physics. Revised and expanded Second Edition. Springer. doi:10.1007/978-3-030-82040-4.
^ Khasminskii, R. Z. (2012). Stochastic Stability of Differential Equations. Springer. doi:10.1007/978-3-642-23280-0.
^ Mil'shtein, G. N. (1974). "Approximate integration of stochastic differential equations". Teoriya Veroyatnostei i ee Primeneniya (in Russian). 19 (3): 583–588.
^ Mil’shtein, G. N. (1975). "Approximate Integration of Stochastic Differential Equations". Theory of Probability & Its Applications. 19 (3): 557–562. doi:10.1137/1119062.
^ Mil'shtein, G. N. (1978). "A method with second order accuracy for the integration of stochastic differential equations". Theory of Probability & Its Applications. 23: 414–419. doi:10.1137/1123045.
^ Mil'shtein, G. N. (1985). "Weak approximation of solutions of systems of stochastic differential equations". Theory of Probability & Its Applications. 30: 706–721. doi:10.1137/1130095.
^ Mil'shtein, G. N. (1987). "A theorem on the order of convergence of mean-square approximations of solutions of systems of stochastic differential equations". Theory of Probability & Its Applications. 32: 809–811. doi:10.1137/1132113.

External links

Grigori N. Milstein, List of publications
Workshop Milstein's method: 50 years on, 30 June - 03 July 2025

[1] Milstein, G. N. (1988). Numerical Integration of Stochastic Differential Equations (in Russian). Ural. State Univ., Sverdlovsk.

[2] Milstein, G. N. (1995). Numerical Integration of Stochastic Differential Equations. Kluwer Academic Publishers. doi:10.1007/978-94-015-8455-5.

[3] Milstein, G. N.; Tretyakov, M. V. (2004). Stochastic Numerics for Mathematical Physics. Springer. doi:10.1007/978-3-662-10063-9.

[4] Milstein, G. N.; Tretyakov, M. V. (2021). Stochastic Numerics for Mathematical Physics. Revised and expanded Second Edition. Springer. doi:10.1007/978-3-030-82040-4.

[5] Khasminskii, R. Z. (2012). Stochastic Stability of Differential Equations. Springer. doi:10.1007/978-3-642-23280-0.

[6] Mil'shtein, G. N. (1974). "Approximate integration of stochastic differential equations". Teoriya Veroyatnostei i ee Primeneniya (in Russian). 19 (3): 583–588.

[7] Mil’shtein, G. N. (1975). "Approximate Integration of Stochastic Differential Equations". Theory of Probability & Its Applications. 19 (3): 557–562. doi:10.1137/1119062.

[8] Mil'shtein, G. N. (1978). "A method with second order accuracy for the integration of stochastic differential equations". Theory of Probability & Its Applications. 23: 414–419. doi:10.1137/1123045.

[9] Mil'shtein, G. N. (1985). "Weak approximation of solutions of systems of stochastic differential equations". Theory of Probability & Its Applications. 30: 706–721. doi:10.1137/1130095.

[10] Mil'shtein, G. N. (1987). "A theorem on the order of convergence of mean-square approximations of solutions of systems of stochastic differential equations". Theory of Probability & Its Applications. 32: 809–811. doi:10.1137/1132113.

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