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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A comparison theorem for solutions of stochastic differential equations and its applications
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by Zhi Yuan Huang PDF
Proc. Amer. Math. Soc. 91 (1984), 611-617 Request permission

Abstract:

A new kind of comparison theorem in which an SDE is compared with two deterministic ODEs is established by means of the generalized sample solutions of SDEs. Using this theorem, we can compare solutions of two SDEs with different diffusion coefficients and obtain some asymptotic estimations for the paths of diffusion processes.
References
  • A. V. Skorohod, Issledovaniya po teorii sluchaĭ nykh protsessov (Stokhasticheskie differentsial′nye uravneniya i predel′nye teoremy dlya protsessov Markova), Izdat. Kiev. Univ., Kiev, 1961 (Russian). MR 0185619
  • A. F. Filippov, Differential equations with discontinuous right-hand side, Mat. Sb. (N.S.) 51 (93) (1960), 99–128 (Russian). MR 0114016
  • Toshio Yamada, On a comparison theorem for solutions of stochastic differential equations and its applications, J. Math. Kyoto Univ. 13 (1973), 497–512. MR 339334, DOI 10.1215/kjm/1250523321
  • Nobuyuki Ikeda and Shinzo Watanabe, A comparison theorem for solutions of stochastic differential equations and its applications, Osaka Math. J. 14 (1977), no. 3, 619–633. MR 471082
  • Halim Doss, Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. H. Poincaré Sect. B (N.S.) 13 (1977), no. 2, 99–125 (French, with English summary). MR 0451404
  • Halim Doss and Erik Lenglart, Sur l’existence, l’unicité et le comportement asymptotique des solutions d’équations différentielles stochastiques, Ann. Inst. H. Poincaré Sect. B (N.S.) 14 (1978), no. 2, 189–214 (French, with English summary). MR 507733
  • Paul Malliavin, Géométrie différentielle stochastique, Séminaire de Mathématiques Supérieures [Seminar on Higher Mathematics], vol. 64, Presses de l’Université de Montréal, Montreal, Que., 1978 (French). Notes prepared by Danièle Dehen and Dominique Michel. MR 540035
  • G. L. O’Brien, A new comparison theorem for solutions of stochastic differential equations, Stochastics 3 (1980), no. 4, 245–249. MR 581039, DOI 10.1080/17442508008833148
  • Toshio Yamada and Yukio Ogura, On the strong comparison theorems for solutions of stochastic differential equations, Z. Wahrsch. Verw. Gebiete 56 (1981), no. 1, 3–19. MR 612157, DOI 10.1007/BF00531971
  • Nobuyuki Ikeda and Shinzo Watanabe, Stochastic differential equations and diffusion processes, 2nd ed., North-Holland Mathematical Library, vol. 24, North-Holland Publishing Co., Amsterdam; Kodansha, Ltd., Tokyo, 1989. MR 1011252
  • Zhi Yuan Huang, Ming Hao Xu, and Ze Cheng Hu, Generalized sample solutions of stochastic differential equations, Wuhan Daxue Xuebao 2 (1981), 11–21 (Chinese, with English summary). MR 651340
  • Philip E. Protter, On the existence, uniqueness, convergence and explosions of solutions of systems of stochastic integral equations, Ann. Probability 5 (1977), no. 2, 243–261. MR 431380, DOI 10.1214/aop/1176995849
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 91 (1984), 611-617
  • MSC: Primary 60H10; Secondary 34F05
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0746100-9
  • MathSciNet review: 746100