Beginning of the Ukrainian School of Probability Theory: A historical sketch
Author:
M. I. Portenko
Translated by:
Andrei Klesov
Journal:
Theor. Probability and Math. Statist. 79 (2009), 1-5
MSC (2000):
Primary 01A70, 01A72
DOI:
https://doi.org/10.1090/S0094-9000-09-00786-8
Published electronically:
December 28, 2009
MathSciNet review:
2494531
Full-text PDF Free Access
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Additional Information
References
- M. M. Bogolyubov and M. M. Krylov, On the Fokker–Planck equations derived in perturbation theory by a method based on the spectral properties of a perturbed Hamiltonian, Zapiski Kafedry Fiziki Akademii Nauk Ukrain. SSR, vol. 4, Kyiv, 1939, pp. 81–157. (Ukrainian)
- S. N. Bernstein, Principes de la théorie des équations différentielles stochastiques, Trudy Matem. Inst. AN SSSR, ser. matem. 5 (1933), 95–124.
- I. I. Gikhman, An influence of a random process on a dynamical system, Naukovi Zapyski Mekh. Mat., Kiev Univ. 5 (1941), 119–132. (Ukrainian)
- I. I. Gikhman, On passing to the limits in dynamical systems, Naukovi Zapyski Mekh. Mat., Kiev Univ. 5 (1941), 141–149. (Ukrainian)
- I. I. Gihman, On a scheme of formation of random processes, Doklady Akad. Nauk SSSR (N. S.) 58 (1947), 961–964 (Russian). MR 0023014
- I. L. Gihman, On some differential equations with random functions, Ukrain. Mat. Žurnal 2 (1950), no. 3, 45–69 (Russian). MR 0048735
- I. I. Gihman, On the theory of differential equations of random processes, Ukrain. Mat. Žurnal 2 (1950), no. 4, 37–63 (Russian). MR 0048736
- I. I. Gihman, On the theory of differential equations of random processes. II, Ukrain. Mat. Žurnal 3 (1951), 317–339 (Russian). MR 0055620
- Kiyosi Itô, Stochastic integral, Proc. Imp. Acad. Tokyo 20 (1944), 519–524. MR 14633
- Kiyosi Itô, On a stochastic integral equation, Proc. Japan Acad. 22 (1946), no. nos. 1-4, 32–35. MR 36958
- Kiyosi Ito, On stochastic differential equations, Mem. Amer. Math. Soc. 4 (1951), 51. MR 40618
- A. V. Skorokhod, Asymptotic methods in the theory of stochastic differential equations, Translations of Mathematical Monographs, vol. 78, American Mathematical Society, Providence, RI, 1989. Translated from the Russian by H. H. McFaden. MR 1020057
References
- M. M. Bogolyubov and M. M. Krylov, On the Fokker–Planck equations derived in perturbation theory by a method based on the spectral properties of a perturbed Hamiltonian, Zapiski Kafedry Fiziki Akademii Nauk Ukrain. SSR, vol. 4, Kyiv, 1939, pp. 81–157. (Ukrainian)
- S. N. Bernstein, Principes de la théorie des équations différentielles stochastiques, Trudy Matem. Inst. AN SSSR, ser. matem. 5 (1933), 95–124.
- I. I. Gikhman, An influence of a random process on a dynamical system, Naukovi Zapyski Mekh. Mat., Kiev Univ. 5 (1941), 119–132. (Ukrainian)
- I. I. Gikhman, On passing to the limits in dynamical systems, Naukovi Zapyski Mekh. Mat., Kiev Univ. 5 (1941), 141–149. (Ukrainian)
- I. I. Gikhman, On a scheme of constructing random processes, Doklady Akad. Nauk SSSR 58 (1947), 961–964. (Russian) MR 0023014 (9:293a)
- I. I. Gikhman, On some differential equations with random functions, Ukrain. Mat. Zhurnal II (1950), no. 3, 45–69. (Russian) MR 0048735 (14:61e)
- I. I. Gikhman, On the theory of differential equations of random processes, Ukrain. Mat. Zhurnal 2 (1950), no. 4, 37–63. (Russian) MR 0048736 (14:61f)
- I. I. Gikhman, On the theory of differential equations of random processes. II, Ukrain. Mat. Zhurnal 3 (1951), 317–339. (Russian) MR 0055620 (14:1101g)
- K. Itô, Stochastic integral, Proc. Imp. Acad., Tokyo 20 (1944), 519–524. MR 0014633 (7:313c)
- K. Itô, On a stochastic integral equation, Proc. Jap. Acad. (1946), no. 1–4, 32–35. MR 0036958 (12:191c)
- K. Itô, On stochastic differential equations, Mem. Amer. Math. Soc. 4 (1951), 1–51. MR 0040618 (12:724a)
- A. V. Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations, Naukova Dumka, Kiev, 1987; English transl., American Mathematical Society, Providence, RI, 1989. MR 1020057 (90i:60038)
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Additional Information
M. I. Portenko
Affiliation:
Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska Street 3, Kyiv 01601, Ukraine
Email:
portenko@imath.kiev.ua
Published electronically:
December 28, 2009
Dedicated:
Dedicated to the 90th birthday anniversary of Iosif Ill’ich Gikhman
Article copyright:
© Copyright 2009
American Mathematical Society
