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Uspekhi Mat. Nauk, 1982, Volume 37, Issue 6(228), Pages 75–95 (Mi umn3945)  

This article is cited in 23 scientific papers (total in 23 papers)

Stochastic partial differential equations and diffusion processes

N. V. Krylov, B. L. Rozovskii


Full text: PDF file (1122 kB)
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English version:
Russian Mathematical Surveys, 1982, 37:6, 81–105

Bibliographic databases:

UDC: 519.21
MSC: 60H15, 60J60, 45E05, 35R30
Received: 18.06.1982

Citation: N. V. Krylov, B. L. Rozovskii, “Stochastic partial differential equations and diffusion processes”, Uspekhi Mat. Nauk, 37:6(228) (1982), 75–95; Russian Math. Surveys, 37:6 (1982), 81–105

Citation in format AMSBIB
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\by N.~V.~Krylov, B.~L.~Rozovskii
\paper Stochastic partial differential equations and diffusion processes
\jour Uspekhi Mat. Nauk
\yr 1982
\vol 37
\issue 6(228)
\pages 75--95
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\transl
\jour Russian Math. Surveys
\yr 1982
\vol 37
\issue 6
\pages 81--105
\crossref{https://doi.org/10.1070/RM1982v037n06ABEH004022}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. L. Daletskii, “Stochastic differential geometry”, Russian Math. Surveys, 38:3 (1983), 97–125  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. Yu. Veretennikov, “Probabilistic problems in the theory of hypoellipticity”, Math. USSR-Izv., 25:3 (1985), 455–473  mathnet  crossref  mathscinet  zmath
    3. A. Germani, M. Piccioni, “Semi-discretization of stochastic partial differential equations on rdby a Finite-element Technique A. Germani”, Stochastics, 23:2 (1988), 131  crossref
    4. Robert J. Elliott, Roland Glowinski, “Approximations to solutions of the zakai filtering equation”, Stochastic Analysis and Applications, 7:2 (1989), 145  crossref
    5. M. Chaleyat-Maurel, D. Michel, E. Pardoux, “Un théorème d'unicité pour l'equation de zakaï”, Stochastics and Stochastic Reports, 29:1 (1990), 1  crossref
    6. Patrick Florchinger, “Existence of a smooth density for the filter in nonlinear filtering with infinite dimensional noise”, Systems & Control Letters, 16:2 (1991), 131  crossref
    7. Xun Yu Zhou, “A duality analysis on stochastic partial differential equations”, Journal of Functional Analysis, 103:2 (1992), 275  crossref
    8. Patrick Florchinger, “Zakai equation of nonlinear filtering with unbounded coefficients. The case of dependent noises”, Systems & Control Letters, 21:5 (1993), 413  crossref
    9. Xun Yu Zhou, “A class of semilinear stochastic partial differential equations and their controls: Existence results”, Stochastic Processes and their Applications, 44:1 (1993), 89  crossref
    10. H. Kunita, “Generalized solutions of a stochastic partial differential equation”, J Theoret Probab, 7:2 (1994), 279  crossref  mathscinet  zmath
    11. H. Salehi, A.V. Skorokhod, “On asymptotic behavior of oscillatory solutions of operator differential equations perturbed by a fast Markov process”, Probabilistic Engineering Mechanics, 11:4 (1996), 251  crossref
    12. Giuseppe Da Parato, “Some remarks about backward itô formula and applications”, Stochastic Analysis and Applications, 16:6 (1998), 993  crossref
    13. Hyek Yoo, “Lp-estimates for stochastic PDEs with discontinuous coefficients”, Stochastic Analysis and Applications, 17:4 (1999), 687  crossref
    14. Yoo H., “Semi-Discretization of Stochastic Partial Differential Equations on R-1 by a Finite-Difference Method”, Math. Comput., 69:230 (2000), 653–666  isi
    15. Marco Ferrante, Marta Sanz-Solé, “SPDEs with coloured noise: Analytic and stochastic approaches”, Probability and Statistics, 10 (2006), 380  crossref  mathscinet  zmath
    16. V. V. Khutortsev, “Application of stochastic equivalence for solving parabolic partial differential equations”, Comput. Math. Math. Phys., 46:3 (2006), 402–412  mathnet  crossref  mathscinet  zmath  elib  elib
    17. Giuseppe Da Prato, Jose-Luis Menaldi, Luciano Tubaro, “Some Results of Backward Itô Formula”, Stochastic Analysis & Applications, 25:3 (2007), 679  crossref
    18. Annika Lang, Pao-Liu Chow, Jurgen Potthoff, “Almost sure convergence of a semidiscrete Milstein scheme for SPDEs of Zakai type”, Stochastics An Int. J. of Probability & Stochastic Processes, 82:3 (2010), 315  crossref
    19. Iyer G., Novikov A., “The Regularizing Effects of Resetting in a Particle System for the Burgers Equation”, Ann. Probab., 39:4 (2011), 1468–1501  crossref  isi
    20. F. S. Nasyrov, E. V. Yureva, “O postroenii i modelirovanii reshenii nekotorykh klassov uravnenii s mnogomernym simmetrichnym integralom”, Ufimsk. matem. zhurn., 4:2 (2012), 114–126  mathnet  mathscinet
    21. E. V. Karachanskaya, “The generalized Itô–Venttsel' formula in the case of a noncentered Poisson measure, a stochastic first integral, and a first integral”, Siberian Adv. Math., 25:3 (2015), 191–205  mathnet  crossref  mathscinet
    22. V. A. Dubko, E. V. Karachanskaya, “Stokhasticheskie pervye integraly, yadra integralnykh invariantov i uravneniya Kolmogorova”, Dalnevost. matem. zhurn., 14:2 (2014), 200–216  mathnet
    23. M.D.. Gunzburger, Lisheng Hou, Ju Ming, “Stochastic Steady-State Navier–Stokes Equations with Additive Random Noise”, J Sci Comput, 2015  crossref
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