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Teoriya Veroyatnostei i ee Primeneniya, 1990, Volume 35, Issue 3, Pages 576–580 (Mi tvp1364)  

This article is cited in 27 scientific papers (total in 27 papers)

Short Communications

A simple proof of the existence of a solution to the Itô equation with monotone coefficients

N. V. Krylov
Received: 05.09.1988
English version:
Theory of Probability and its Applications, 1990, Volume 35, Issue 3, Pages 583–587
DOI: https://doi.org/10.1137/1135082
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: N. V. Krylov, “A simple proof of the existence of a solution to the Itô equation with monotone coefficients”, Teor. Veroyatnost. i Primenen., 35:3 (1990), 576–580; Theory Probab. Appl., 35:3 (1990), 583–587
Citation in format AMSBIB
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\paper A~simple proof of the existence of a~solution to the It\^o equation with monotone coefficients
\jour Teor. Veroyatnost. i Primenen.
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\issue 3
\pages 576--580
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\transl
\jour Theory Probab. Appl.
\yr 1990
\vol 35
\issue 3
\pages 583--587
\crossref{https://doi.org/10.1137/1135082}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1990GN64500022}
Linking options:
  • https://www.mathnet.ru/eng/tvp1364
  • https://www.mathnet.ru/eng/tvp/v35/i3/p576
  • This publication is cited in the following 27 articles:
    1. Xicheng Zhang, “Compound Poisson particle approximation for McKean–Vlasov SDEs”, IMA Journal of Numerical Analysis, 2025  crossref
    2. Predrag Pilipovic, Adeline Samson, Susanne Ditlevsen, “Parameter estimation in nonlinear multivariate stochastic differential equations based on splitting schemes”, Ann. Statist., 52:2 (2024)  crossref
    3. Fangfang Shen, Huaqin Peng, “Existence and uniqueness of solutions for stochastic differential equations with locally one-sided Lipschitz condition”, MATH, 9:8 (2024), 22578  crossref
    4. Dong-Young Lim, Ariel Neufeld, Sotirios Sabanis, Ying Zhang, “Langevin Dynamics Based Algorithm e-THεO POULA for Stochastic Optimization Problems with Discontinuous Stochastic Gradient”, Mathematics of OR, 2024  crossref
    5. Dong-Young Lim, Ariel Neufeld, Sotirios Sabanis, Ying Zhang, “Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation function”, IMA Journal of Numerical Analysis, 2023  crossref
    6. Konstantinos Dareiotis, Máté Gerencsér, Khoa Lê, “Quantifying a convergence theorem of Gyöngy and Krylov”, Ann. Appl. Probab., 33:3 (2023)  crossref
    7. Evelyn Buckwar, Adeline Samson, Massimiliano Tamborrino, Irene Tubikanec, “A splitting method for SDEs with locally Lipschitz drift: Illustration on the FitzHugh-Nagumo model”, Applied Numerical Mathematics, 179 (2022), 191  crossref
    8. Yunzhang Li, Shanjian Tang, “Approximation of BSDEs with super-linearly growing generators by Euler's polygonal line method: A simple proof of the existence”, Systems & Control Letters, 153 (2021), 104952  crossref
    9. Li Tan, Chenggui Yuan, “A note on strong convergence of implicit scheme for SDEs under local one-sided Lipschitz conditions”, International Journal of Computer Mathematics, 98:2 (2021), 238  crossref
    10. Latifa Debbi, “Fractional Stochastic Active Scalar Equations Generalizing the Multi-Dimensional Quasi-Geostrophic & 2D-Navier–Stokes Equations: The General Case”, J. Math. Fluid Mech., 22:4 (2020)  crossref
    11. Andrei Cozma, Christoph Reisinger, “Strong Convergence Rates for Euler Approximations to a Class of Stochastic Path-Dependent Volatility Models”, SIAM J. Numer. Anal., 56:6 (2018), 3430  crossref
    12. Xueyan Zhao, Feiqi Deng, “A New Type of Stability Theorem for Stochastic Systems With Application to Stochastic Stabilization”, IEEE Trans. Automat. Contr., 61:1 (2016), 240  crossref
    13. Latifa Debbi, “Well-Posedness of the Multidimensional Fractional Stochastic Navier–Stokes Equations on the Torus and on Bounded Domains”, J. Math. Fluid Mech., 18:1 (2016), 25  crossref
    14. Jean-François Chassagneux, Antoine Jacquier, Ivo Mihaylov, “An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz Coefficients”, SIAM J. Finan. Math., 7:1 (2016), 993  crossref
    15. Martin Hairer, Martin Hutzenthaler, Arnulf Jentzen, “Loss of regularity for Kolmogorov equations”, Ann. Probab., 43:2 (2015)  crossref
    16. Chaman Kumar, Sotirios Sabanis, “Strong Convergence of Euler Approximations of Stochastic Differential Equations with Delay Under Local Lipschitz Condition”, Stochastic Analysis and Applications, 32:2 (2014), 207  crossref
    17. Martin Hutzenthaler, Arnulf Jentzen, Peter E. Kloeden, “Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations”, Ann. Appl. Probab., 23:5 (2013)  crossref
    18. Ji Cheng Liu, “Rate of convergence of Euler's approximations for SDEs with non-Lipschitz coefficients”, Acta. Math. Sin.-English Ser., 29:8 (2013), 1555  crossref
    19. Istvan Gyöngy, Sotirios Sabanis, “A Note on Euler Approximations for Stochastic Differential Equations with Delay”, Appl Math Optim, 68:3 (2013), 391  crossref
    20. Jerzy Motyl, “Stochastic Itô inclusion with upper separated multifunctions”, Journal of Mathematical Analysis and Applications, 400:2 (2013), 505  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Теория вероятностей и ее применения Theory of Probability and its Applications
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