Edit Profile (opens in new tab) Krylov, Nicolaĭ Vladimirovich Co-Author Distance Author ID: krylov.nicolai-v Published as: Krylov, N. V.; Krylov, Nicolai V.; Krylov, Nicolai; Krylov, N.; Krylov, Nicolaï more...less Further Spellings: Крылов Николай Владимирович Homepage: http://www.math.umn.edu/~nkrylov/ External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru · dblp · GND · IdRef Documents Indexed: 357 Publications since 1964, including 17 Books and 14 Additional arXiv Preprints 3 Contributions as Editor Biographic References: 1 Publication Co-Authors: 35 Co-Authors with 102 Joint Publications 1,194 Co-Co-Authors all top 5 Co-Authors 256 single-authored 24 Gyöngy, István 13 Rozovskii, Boris L. 10 Röckner, Michael 9 Dong, Hongjie 8 Bogachev, Vladimir Igorevich 6 Safonov, Mikhail V. 4 Khas’minskiĭ, Rafail Zalmanovich 4 Liptser, Robert 4 Veretennikov, Alexander Yu. 3 Genis, I. L. 3 Kim, Doyoon 3 Priola, Enrico 3 Shiryaev, Al’bert Nikolaevich 3 Yushkevich, Aleksandr Adol’fovich 2 Anulova, Svetlana 2 Jain, Naresh C. 2 Kim, KyeongHun 2 Lototsky, Sergey V. 2 Miroshnichenko, T. P. 2 Novikov, Aleksandr Aleksandrovich 2 Pragarauskas, Henrikas 2 Zatezalo, Aleksandar 1 Alyushina, L. A. 1 Da Prato, Giuseppe 1 Fristedt, Bert E. 1 Gerencsér, Máté 1 Kabanov, Yuriĭ Mikhaĭlovich 1 Li, Xu 1 Luo, Jun 1 Moshchuk, Nickolay K. 1 Paragarauskas, H. 1 Shaposhnikov, Stanislav V. 1 Ural’tseva, Nina Nikolaevna 1 Wang, Teng 1 Yastrzhembskiy, Timur 1 Zabczyk, Jerzy 1 Zvonkin, Alexander K. all top 5 Serials 16 Theory of Probability and its Applications 16 Mathematics of the USSR. Izvestiya 14 Probability Theory and Related Fields 14 Mathematics of the USSR, Sbornik 13 Matematicheskiĭ Sbornik. Novaya Seriya 13 Communications in Partial Differential Equations 13 SIAM Journal on Mathematical Analysis 12 Stochastic Processes and their Applications 10 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 9 The Annals of Probability 9 Applied Mathematics and Optimization 8 Teoriya Veroyatnosteĭ i eë Primeneniya 8 St. Petersburg Mathematical Journal 7 Soviet Mathematics. Doklady 6 Journal of Functional Analysis 6 Journal of Mathematical Sciences (New York) 6 Stochastic and Partial Differential Equations. Analysis and Computations 5 Potential Analysis 5 Methods and Applications of Analysis 4 Mathematics of Computation 4 Siberian Mathematical Journal 4 Sibirskiĭ Matematicheskiĭ Zhurnal 4 Transactions of the American Mathematical Society 4 Electronic Journal of Probability 3 Lithuanian Mathematical Journal 3 Uspekhi Matematicheskikh Nauk [N. S.] 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Stochastics and Stochastics Reports 3 Graduate Studies in Mathematics 2 Mathematical Notes 2 Russian Mathematical Surveys 2 Stochastics 2 Ukrainian Mathematical Journal 2 Ukraïns’kyĭ Matematychnyĭ Zhurnal 2 Differentsial’nye Uravneniya 2 Differential Equations 2 Illinois Journal of Mathematics 2 Journal of Soviet Mathematics 2 Proceedings of the American Mathematical Society 2 Differential and Integral Equations 2 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 2 Journal of Dynamics and Differential Equations 2 Topological Methods in Nonlinear Analysis 2 Calculus of Variations and Partial Differential Equations 2 NoDEA. Nonlinear Differential Equations and Applications 2 Doklady Mathematics 2 Mathematical Surveys and Monographs 2 Applications of Mathematics 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Matematicheskie Zametki 1 Moscow University Mathematics Bulletin 1 Collectanea Mathematica 1 Transactions of the Moscow Mathematical Society 1 Trudy Moskovskogo Matematicheskogo Obshchestva 1 Selecta Mathematica Sovietica 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Litovskiĭ Matematicheskiĭ Sbornik 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Izvestiya Rossiĭskoĭ Akademii Nauk. Seriya Matematicheskaya 1 Russian Academy of Sciences. Izvestiya. Mathematics 1 Trudy Seminara Imeni I. G. Petrovskogo 1 Electronic Journal of Differential Equations (EJDE) 1 Ulam Quarterly 1 Journal of Convex Analysis 1 Statistical Inference for Stochastic Processes 1 Communications in Contemporary Mathematics 1 Theory of Stochastic Processes 1 Discrete and Continuous Dynamical Systems. Series B 1 Communications on Pure and Applied Analysis 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Stochastics 1 Journal of Mathematical Physics, Analysis, Geometry 1 Complex Variables and Elliptic Equations 1 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya 1 Lecture Notes in Mathematics 1 Mathematics and Its Applications. Soviet Series 1 Translations of Mathematical Monographs 1 Student Mathematical Library 1 Analysis and Mathematical Physics 1 Mathematics in Engineering all top 5 Fields 196 Probability theory and stochastic processes (60-XX) 193 Partial differential equations (35-XX) 50 Systems theory; control (93-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 24 Numerical analysis (65-XX) 10 Functional analysis (46-XX) 9 Statistics (62-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Difference and functional equations (39-XX) 7 Operator theory (47-XX) 5 Real functions (26-XX) 5 Ordinary differential equations (34-XX) 5 Operations research, mathematical programming (90-XX) 4 General and overarching topics; collections (00-XX) 3 Measure and integration (28-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Convex and discrete geometry (52-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Potential theory (31-XX) 1 Integral equations (45-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 291 Publications have been cited 6,713 times in 4,030 Documents Cited by ▼ Year ▼ Controlled diffusion processes. Transl. by A. B. Aries. Zbl 0459.93002 Krylov, N. V. 306 1980 Lectures on elliptic and parabolic equations in Hölder spaces. Zbl 0865.35001 Krylov, N. V. 290 1996 Nonlinear elliptic and parabolic equations of the second order. Transl. from the Russian by P. L. Buzytsky. Zbl 0619.35004 Krylov, N. V. 276 1987 Lectures on elliptic and parabolic equations in Sobolev spaces. Zbl 1147.35001 Krylov, N. V. 253 2008 Strong solutions of stochastic equations with singular time dependent drift. Zbl 1072.60050 Krylov, N. V.; Röckner, M. 238 2005 Existence of strong solutions for Itô’s stochastic equations via approximations. Zbl 0847.60038 Gyöngy, István; Krylov, Nicolai 237 1996 Fokker-Planck-Kolmogorov equations. Zbl 1342.35002 Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael; Shaposhnikov, Stanislav V. 184 2015 Parabolic and elliptic equations with VMO coefficients. Zbl 1114.35079 Krylov, N. V. 176 2007 An analytic approach to SPDEs. Zbl 0933.60073 Krylov, N. V. 171 1999 Stochastic evolution equations. Zbl 0462.60060 Krylov, N. V.; Rozovskij, B. L. 161 1981 On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions. Zbl 0997.35012 Bogachev, V. I.; Krylov, N. V.; Röckner, M. 138 2001 Eine gewisse Eigenschaft der Lösungen parabolischer Gleichungen mit meßbaren Koeffizienten. Zbl 0439.35023 Krylov, N. V.; Safonov, M. V. 131 1980 Bounded inhomogeneous elliptic and parabolic equations. Zbl 0511.35002 Krylov, N. V. 124 1982 Some new results in the theory of controlled diffusion processes. Zbl 0436.93055 Krylov, N. V. 119 1980 A certain property of solutions of parabolic equations with measurable coefficients. Zbl 0464.35035 Krylov, N. V.; Safonov, M. V. 114 1981 Nonlinear elliptic and parabolic equations of second order. (Нелинейные ѐллиптические и параболические уравнения второго порядка.) Zbl 0586.35002 Krylov, N. V. 80 1985 On the rate of convergence of finite-difference approximations for Bellman’s equations with variable coefficients. Zbl 0971.65081 Krylov, N. V. 80 2000 Controlled processes of diffusion type. (Управляемые процессы диффузионного типа.) Zbl 0513.60043 Krylov, N. V. 79 1977 Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others. Zbl 1138.35308 Kim, Doyoon; Krylov, N. V. 77 2007 Introduction to the theory of diffusion processes. Transl. from the Russian by V. Khidekel a. G. Pasechnik. Zbl 0844.60050 Krylov, N. V. 74 1995 Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms. Zbl 1133.35052 Krylov, N. V. 72 2007 On stochastic equations with respect to semimartingales I. Zbl 0439.60061 Gyöngy, I.; Krylov, N. V. 70 1980 On stochastics equations with respect to semimartingales. II. Ito formula in Banach spaces. Zbl 0481.60060 Gyoengy, I.; Krylov, N. V. 69 1982 On the selection of a Markov process from a system of processes and the construction of quasi-diffusion processes. Zbl 0295.60057 Krylov, N. V. 68 1974 An estimate of the probability that a diffusion process hits a set of positive measure. Zbl 0459.60067 Krylov, N. V.; Safonov, M. V. 67 1979 Elliptic and parabolic equations for measures. Zbl 1194.35481 Bogachev, V. I.; Krylov, N. V.; Röckner, M. 64 2009 On \(L_ p\)-theory of stochastic partial differential equations in the whole space. Zbl 0846.60061 Krylov, N. V. 62 1996 Parabolic equations with measurable coefficients. Zbl 1124.35024 Kim, Doyoon; Krylov, N. V. 59 2007 On the general notion of fully nonlinear second-order elliptic equations. Zbl 0832.35042 Krylov, N. V. 58 1995 Boundedly nonhomogeneous elliptic and parabolic equations. Zbl 0529.35026 Krylov, N. V. 57 1983 Controlled diffusion processes. Translated by A. B. Aries. Reprint of the 1980 ed. Zbl 1171.93004 Krylov, N. V. 54 2009 On the Cauchy problem for linear stochastic partial differential equations. Zbl 0396.60058 Krylov, N. V.; Rozovskii, B. L. 54 1977 A \(W_ 2^ n\)-theory of the Dirichlet problem for SPDEs in general smooth domains. Zbl 0794.60062 Krylov, N. V. 53 1994 Boundedly nonhomogeneous elliptic and parabolic equations in a domain. Zbl 0578.35024 Krylov, N. V. 53 1984 On the splitting-up method and stochastic partial differential equations. Zbl 1028.60058 Gyöngy, István; Krylov, Nicolai 52 2003 Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation. Zbl 0362.35038 Krylov, N. V. 52 1976 Second-order elliptic equations with variably partially VMO coefficients. Zbl 1171.35352 Krylov, N. V. 51 2009 On the Itô–Wentzell formula for distribution-valued processes and related topics. Zbl 1238.60060 Krylov, N. V. 47 2011 A Sobolev space theory of SPDEs with constant coefficients in a half space. Zbl 0943.60047 Krylov, N. V.; Lototsky, S. V. 46 1999 Stochastic evolution equations. Zbl 1130.60069 Krylov, Nicolai V.; Rozovskii, Boris L. 42 2007 Weighted Sobolev spaces and Laplace’s equation and the heat equations in a half space. Zbl 0934.35032 Krylov, N. V. 42 1999 Itô’s formula for the \(L _{p }\)-norm of stochastic \({W^{1}_{p}}\)-valued processes. Zbl 1232.60050 Krylov, N. V. 41 2010 Elliptic and parabolic second-order PDEs with growing coefficients. Zbl 1195.35160 Krylov, N. V.; Priola, E. 41 2010 Some properties of traces for stochastic and deterministic parabolic weighted Sobolev spaces. Zbl 0980.60091 Krylov, N. V. 40 2001 On the Sobolev space theory of parabolic and elliptic equations in \(C^{1}\) domains. Zbl 1083.35041 Kim, Kyeong-Hun; Krylov, N. V. 40 2004 The rate of convergence of finite-difference approximations for Bellman equations with Lipschitz coefficients. Zbl 1087.65100 Krylov, Nicolai V. 40 2005 The heat equation in \(L_{q}((0,T),L_{p})\)-spaces with weights. Zbl 0979.35060 Krylov, N. V. 37 2001 On Ito’s stochastic integral equations. Zbl 0281.60066 Krylov, N. V. 36 1969 A relatively short proof of Itô’s formula for SPDEs and its applications. Zbl 1274.60204 Krylov, N. V. 35 2013 On Kolmogorov’s equations for finite dimensional diffusions. Zbl 0943.60070 Krylov, N. V. 35 1999 Approximating value functions for controlled degenerate diffusion processes by using piece-wise constant policies. Zbl 1044.93546 Krylov, N. V. 33 1999 Control of a solution of a stochastic integral equation. Zbl 0265.60055 Krylov, N. V. 32 1972 Introduction to the theory of random processes. Zbl 1008.60001 Krylov, N. V. 32 2002 On weak uniqueness for some diffusions with discontinuous coefficients. Zbl 1073.60064 Krylov, N. V. 31 2004 On the rate of convergence of splitting-up approximations for SPDEs. Zbl 1038.60057 Gyöngy, István; Krylov, Nicolai 28 2003 A Sobolev space theory of SPDE with constant coefficients on a half line. Zbl 0928.60042 Krylov, N. V.; Lototsky, S. V. 28 1999 Sobolev and viscosity solutions for fully nonlinear elliptic and parabolic equations. Zbl 1401.35001 Krylov, N. V. 27 2018 On the rate of convergence of finite-difference approximations for Bellman’s equations. Zbl 0902.65035 Krylov, N. V. 26 1997 A simple proof of the existence of a solution of Itô’s equation with monotone coefficients. Zbl 0735.60061 Krylov, N. V. 26 1990 Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces. Zbl 1418.35211 Dong, Hongjie; Krylov, N. V. 26 2019 A generalization of the Littlewood-Paley inequality and some other results related to stochastic partial differential equations. Zbl 0870.42005 Krylov, N. V. 25 1994 The rate of convergence of finite-difference approximations for parabolic bellman equations with Lipschitz coefficients in cylindrical domains. Zbl 1127.65068 Dong, Hongjie; Krylov, Nicolai V. 24 2007 Elliptic regularity and essential self-adjointness of Dirichlet operators on \(\mathbb{R}^n\). Zbl 0901.35017 Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael 24 1997 On the existence of \(W^2_p\) solutions for fully nonlinear elliptic equations under relaxed convexity assumptions. Zbl 1277.35172 Krylov, N. V. 23 2013 An inequality in the theory of stochastic integrals. Zbl 0238.60038 Krylov, N. V. 22 1971 Regularity of invariant measures: The case of non-constant diffusion part. Zbl 0929.60039 Bogachev, V. I.; Krylov, N.; Röckner, M. 20 1996 On averaging principle for diffusion processes with null-recurrent fast component. Zbl 1053.60060 Khasminskii, R.; Krylov, N. 20 2001 On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains. Zbl 1278.35133 Dong, Hongjie; Krylov, N. V.; Li, Xu 20 2013 On estimates of the maximum of a solution of a parabolic equation and estimates of the distribution of a semimartingale. Zbl 0625.35041 Krylov, N. V. 20 1987 On diffusion processes with drift in \(L_d\). Zbl 1480.60239 Krylov, N. V. 20 2021 Über stochastische Evolutionsgleichungen. Zbl 0436.60047 Krylov, N. V.; Rozovskij, B. L. 19 1979 On degenerate nonlinear elliptic equations. Zbl 0525.35038 Krylov, N. V. 19 1983 On the solvability of degenerate stochastic partial differential equations in Sobolev spaces. Zbl 1310.60094 Gerencsér, Máté; Gyöngy, István; Krylov, Nicolai 19 2015 Maximum principle for SPDEs and its applications. Zbl 1135.60039 Krylov, Nicolai V. 18 2007 Stochastic partial differential equations and diffusion processes. Zbl 0518.60072 Krylov, N. V.; Rozovskij, B. L. 18 1982 Accelerated finite difference schemes for linear stochastic partial differential equations in the whole space. Zbl 1222.65009 Gyöngy, István; Krylov, Nicolai 18 2010 On time inhomogeneous stochastic Itô equations with drift in \(L_{D+1}\). Zbl 1483.60083 Krylov, N. V. 18 2021 Elliptic equations for measures: regularity and global bounds of densities. Zbl 1206.35242 Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael 17 2006 Characteristics of degenerate second-order parabolic Ito equations. Zbl 0584.60068 Krylov, N. V.; Rozovskij, B. L. 17 1986 SPDEs in \(L_q(\mskip-2mu(0,\tau], L_p)\) spaces. Zbl 0963.60053 Krylov, N. V. 17 2000 On stochastic equations with drift in \({L_d}\). Zbl 1489.60102 Krylov, N. V. 17 2021 On conditional distributions of diffusion processes. Zbl 0402.60077 Krylov, N. V.; Rozovskii, B. L. 17 1978 Second-order elliptic and parabolic equations with \(B(\mathbb R^2, \mathrm{VMO})\) coefficients. Zbl 1207.35174 Dong, Hongjie; Krylov, N. V. 16 2010 Fully nonlinear second order elliptic equations: recent development. Zbl 1033.35036 Krylov, Nicolai V. 16 1997 On the Calderón-Zygmund theorem with applications to parabolic equations. Zbl 1011.35033 Krylov, N. V. 16 2002 On characteristics of the degenerate second order Ito parabolic equations. Zbl 0503.60066 Krylov, N. V.; Rozovskij, B. L. 15 1982 On strong solutions of stochastic differential equations. Zbl 0481.60062 Zvonkin, A. K.; Krylov, N. V. 15 1975 Some properties of weighted Sobolev spaces in \(\mathbb{R}_+^d\). Zbl 0962.46016 Krylov, Nicolai V. 15 1999 On the foundation of the \(L_p\)-theory of stochastic partial differential equations. Zbl 1165.60331 Krylov, Nicolai V. 15 2006 Folgen konvexer Funktionen und Abschätzungen des Maximums der Lösung einer parabolischen Gleichung. Zbl 0354.35052 Krylov, N. V. 15 1976 On Shige Peng’s central limit theorem. Zbl 1433.60013 Krylov, N. V. 15 2020 On the first integrals and Liouville equations for diffusion processes. Zbl 0474.60049 Krylov, N. V.; Rozovskii, B. L. 14 1981 Parabolic equations in \(L_p\)-spaces with mixed norms. Zbl 1032.35046 Krylov, N. V. 14 2003 Smoothness of the value function for a controlled diffusion process in a domain. Zbl 0701.93054 Krylov, N. V. 13 1990 Rate of convergence of finite-difference approximations for degenerate linear parabolic equations with \(C^1\) and \(C^2\) coefficients. Zbl 1085.65087 Dong, Hongjie; Krylov, Nicolai V. 13 2005 An accelerated splitting-up method for parabolic equations. Zbl 1101.35038 Gyöngy, István; Krylov, Nicolai 13 2005 On explicit formulas for solutions of stochastic equations. Zbl 0376.60067 Veretennikov, A. Yu.; Krylov, N. V. 13 1978 Some \(L_{p}\)-estimates for elliptic and parabolic operators with measurable coefficients. Zbl 1258.35069 Krylov, N. V. 13 2012 Über das Cauchyproblem für lineare stochastische partielle Differentialgleichungen. Zbl 0371.60076 Krylov, N. V.; Rozovskii, B. L. 13 1977 On estimates for the derivatives of solutions of nonlinear parabolic equations. Zbl 0598.35057 Krylov, N. V. 13 1984 On weak and strong solutions of time inhomogeneous Itô’s equations with VMO diffusion and Morrey drift. Zbl 07963483 Krylov, N. V. 1 2025 On parabolic equations in Morrey spaces with VMO \(a\) and Morrey \(b\), \(c\). Zbl 07974587 Krylov, N. V. 1 2025 On parabolic Adams’s, the Chiarenza-Frasca theorems, and some other results related to parabolic Morrey spaces. Zbl 1542.35215 Krylov, Nicolai 7 2023 On potentials of Itô’s processes with drift in \(L_{d+1}\). Zbl 1533.60090 Krylov, N. V. 4 2023 Elliptic equations in Sobolev spaces with Morrey drift and the zeroth-order coefficients. Zbl 1522.35184 Krylov, N. V. 3 2023 On diffusion processes with drift in \(L_{d+1}\). Zbl 1543.60067 Krylov, N. V. 2 2023 On nondegenerate Itô processes with moderated drift. Zbl 1524.60112 Krylov, N. V. 2 2023 On diffusion processes with drift in a Morrey class containing \(L_{d+2}\). Zbl 1543.60068 Krylov, N. V. 2 2023 On strong solutions of Itô’s equations with \(D \sigma\) and \(b\) in Morrey classes containing \(L_d\). Zbl 07793390 Krylov, N. V. 2 2023 Estimates in \(L_p\) for solutions of SPDEs with coefficients in Morrey classes. Zbl 1534.60085 Krylov, N. V. 1 2023 On the heat equation with drift in \(L_{d+1}\). Zbl 1510.35090 Krylov, N. V. 4 2022 Linear and fully nonlinear elliptic equations with Morrey drift. Zbl 1511.35103 Krylov, N. V. 3 2022 Some properties of solutions of Itô equations with drift in \(L_{d+1}\). Zbl 1494.60065 Krylov, N. V. 3 2022 Aleksandrov’s estimates for elliptic equations with drift in Morrey spaces containing \(L_d\). Zbl 1482.35057 Dong, Hongjie; Krylov, N. V. 3 2022 Existence of strong solutions for Itô’s stochastic equations via approximations: revisited. Zbl 1499.60187 Gyöngy, I.; Krylov, N. V. 3 2022 On diffusion processes with drift in \(L_d\). Zbl 1480.60239 Krylov, N. V. 20 2021 On time inhomogeneous stochastic Itô equations with drift in \(L_{D+1}\). Zbl 1483.60083 Krylov, N. V. 18 2021 On stochastic equations with drift in \({L_d}\). Zbl 1489.60102 Krylov, N. V. 17 2021 On strong solutions of Itô’s equations with \(\sigma\in W_{\mathtt{d}}^1\) and \(\mathtt{b}\in{L_{\mathtt{d}}}\). Zbl 1497.60076 Krylov, N. V. 12 2021 Elliptic equations with VMO \(a,b\in L_d\), and \(c\in L_{d/2}\). Zbl 1460.35069 Krylov, N. V. 11 2021 Rubio de Francia extrapolation theorem and related topics in the theory of elliptic and parabolic equations. A survey. Zbl 1468.35110 Krylov, N. V. 7 2021 On stochastic Itô processes with drift in \(L_d\). Zbl 1469.60186 Krylov, N. V. 5 2021 A review of some new results in the theory of linear elliptic equations with drift in \(L_d\). Zbl 1461.35002 Krylov, N. V. 2 2021 On Shige Peng’s central limit theorem. Zbl 1433.60013 Krylov, N. V. 15 2020 Linear and fully nonlinear elliptic equations with \(L_d\)-drift. Zbl 1460.35141 Krylov, Nicolai V. 11 2020 Weighted Aleksandrov estimates: PDE and stochastic versions. Zbl 1437.35206 Krylov, N. V. 1 2020 Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces. Zbl 1418.35211 Dong, Hongjie; Krylov, N. V. 26 2019 All functions are locally s-harmonic up to a small error. Zbl 1447.35358 Krylov, N. V. 4 2019 A few comments on a result of A. Novikov and Girsanov’s theorem. Zbl 1492.60113 Krylov, N. V. 3 2019 Sobolev and viscosity solutions for fully nonlinear elliptic and parabolic equations. Zbl 1401.35001 Krylov, N. V. 27 2018 \(C^{1+\alpha}\)-regularity of viscosity solutions of general nonlinear parabolic equations. Zbl 1402.35061 Krylov, N. V. 6 2018 On the existence of \(W_p^{1, 2}\) solutions for fully nonlinear parabolic equations under either relaxed or no convexity assumptions. Zbl 1405.35083 Krylov, N. V. 4 2018 Uniqueness for \(L_{p}\)-viscosity solutions for uniformly parabolic Isaacs equations with measurable lower order terms. Zbl 1394.35231 Krylov, N. V. 3 2018 On the existence of \(W_p^2\) solutions for fully nonlinear elliptic equations under either relaxed or no convexity assumptions. Zbl 1376.35049 Krylov, N. V. 11 2017 Poisson stochastic process and basic Schauder and Sobolev estimates in the theory of parabolic equations. Zbl 1375.35551 Krylov, N. V.; Priola, Enrico 6 2017 On nonequivalence of regular boundary points for second-order elliptic operators. Zbl 1379.35099 Krylov, N. V.; Yastrzhembskiy, Timur 1 2017 Hörmander’s theorem for stochastic partial differential equations. Zbl 1439.60061 Krylov, N. V. 7 2016 On parabolic equations in one space dimension. Zbl 1346.35081 Krylov, N. V. 6 2016 Fokker-Planck-Kolmogorov equations. Zbl 1342.35002 Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael; Shaposhnikov, Stanislav V. 184 2015 On the solvability of degenerate stochastic partial differential equations in Sobolev spaces. Zbl 1310.60094 Gerencsér, Máté; Gyöngy, István; Krylov, Nicolai 19 2015 On the rate of convergence of finite-difference approximations for elliptic Isaacs equations in smooth domains. Zbl 1331.65122 Krylov, N. V. 11 2015 To the theory of viscosity solutions for uniformly parabolic Isaacs equations. Zbl 1329.35170 Krylov, N. V. 3 2015 Hypoellipticity for filtering problems of partially observable diffusion processes. Zbl 1317.60098 Krylov, N. V. 3 2015 Approximating the value functions for stochastic differential games with the ones having bounded second derivatives. Zbl 1302.49053 Krylov, N. V. 1 2015 On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains and the Isaacs equations. Zbl 1290.91022 Krylov, N. V. 10 2014 On \(C^{1+\alpha}\) regularity of solutions of Isaacs parabolic equations with VMO coefficients. Zbl 1304.35173 Krylov, N. V. 8 2014 On the rate of convergence of difference approximations for uniformly nondegenerate elliptic Bellman’s equations. Zbl 1297.65073 Krylov, N. V. 7 2014 Hörmander’s theorem for parabolic equations with coefficients measurable in the time variable. Zbl 1288.35315 Krylov, N. V. 6 2014 On regularity properties and approximations of value functions for stochastic differential games in domains. Zbl 1336.91020 Krylov, N. V. 5 2014 To the theory of viscosity solutions for uniformly elliptic Isaacs equations. Zbl 1302.35171 Krylov, N. V. 3 2014 On the independence of the value function for stochastic differential games of the probability space. Zbl 1307.91033 Krylov, N. V. 2 2014 On the fundamental matrix solution for higher-order parabolic systems. Zbl 1319.35075 Boccia, S.; Krylov, N. V. 1 2014 A relatively short proof of Itô’s formula for SPDEs and its applications. Zbl 1274.60204 Krylov, N. V. 35 2013 On the existence of \(W^2_p\) solutions for fully nonlinear elliptic equations under relaxed convexity assumptions. Zbl 1277.35172 Krylov, N. V. 23 2013 On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains. Zbl 1278.35133 Dong, Hongjie; Krylov, N. V.; Li, Xu 20 2013 On the existence of smooth solutions for fully nonlinear parabolic equations with measurable “coefficients” without convexity assumptions. Zbl 1479.35526 Dong, Hongjie; Krylov, N. V. 9 2013 On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains. Zbl 1287.49027 Krylov, N. V. 5 2013 An ersatz existence theorem for fully nonlinear parabolic equations without convexity assumptions. Zbl 1295.35262 Krylov, N. V. 4 2013 Interior estimates for second-order differences of solutions of finite-difference elliptic Bellman’s equations. Zbl 1269.49050 Krylov, N. V. 1 2013 Some \(L_{p}\)-estimates for elliptic and parabolic operators with measurable coefficients. Zbl 1258.35069 Krylov, N. V. 13 2012 On the existence of smooth solutions for fully nonlinear elliptic equations with measurable “coefficients” without convexity assumptions. Zbl 1285.35033 Krylov, Nicolai V. 11 2012 Interior estimates for the first-order differences for finite-difference approximations for elliptic Bellman’s equations. Zbl 1244.49053 Krylov, N. V. 2 2012 On the Itô–Wentzell formula for distribution-valued processes and related topics. Zbl 1238.60060 Krylov, N. V. 47 2011 On a representation of fully nonlinear elliptic operators in terms of pure second order derivatives and its applications. Zbl 1290.35099 Krylov, N. V. 10 2011 Filtering equations for partially observable diffusion processes with Lipschitz continuous coefficients. Zbl 1223.93112 Krylov, N. V. 6 2011 Filtering partially observable diffusions up to the exit time from a domain. Zbl 1233.62168 Krylov, N. V.; Wang, Teng 5 2011 Accelerated finite difference schemes for second order degenerate elliptic and parabolic problems in the whole space. Zbl 1223.65068 Gyöngy, István; Krylov, Nicolai 5 2011 Accelerated numerical schemes for PDEs and SPDEs. Zbl 1221.65222 Gyöngy, István; Krylov, Nicolai 2 2011 On divergence form second-order PDEs with growing coefficients in \(W^{1}_{p}\) spaces without weights. Zbl 1254.35108 Krylov, N. V. 1 2011 Itô’s formula for the \(L _{p }\)-norm of stochastic \({W^{1}_{p}}\)-valued processes. Zbl 1232.60050 Krylov, N. V. 41 2010 Elliptic and parabolic second-order PDEs with growing coefficients. Zbl 1195.35160 Krylov, N. V.; Priola, E. 41 2010 Accelerated finite difference schemes for linear stochastic partial differential equations in the whole space. Zbl 1222.65009 Gyöngy, István; Krylov, Nicolai 18 2010 Second-order elliptic and parabolic equations with \(B(\mathbb R^2, \mathrm{VMO})\) coefficients. Zbl 1207.35174 Dong, Hongjie; Krylov, N. V. 16 2010 On Bellman’s equations with VMO coefficients. Zbl 1208.35052 Krylov, Nicolai V. 12 2010 About an example of N. N, Ural’tseva and weak uniqueness for elliptic operators. Zbl 1387.35149 Krylov, N. V. 3 2010 On divergence form SPDEs with growing coefficients in \(W^{1}_{2}\) spaces without weights. Zbl 1218.60057 Krylov, N. V. 3 2010 Kalman-Bucy filter and SPDEs with growing lower-order coefficients in \(W_{p}^{1}\) spaces without weights. Zbl 1260.60122 Krylov, N. V. 1 2010 Elliptic and parabolic equations for measures. Zbl 1194.35481 Bogachev, V. I.; Krylov, N. V.; Röckner, M. 64 2009 Controlled diffusion processes. Translated by A. B. Aries. Reprint of the 1980 ed. Zbl 1171.93004 Krylov, N. V. 54 2009 Second-order elliptic equations with variably partially VMO coefficients. Zbl 1171.35352 Krylov, N. V. 51 2009 On divergence form SPDEs with VMO coefficients. Zbl 1195.60091 Krylov, N. V. 9 2009 On divergence form SPDEs with VMO coefficients in a half space. Zbl 1165.60330 Krylov, N. V. 6 2009 On linear elliptic and parabolic equations with growing drift in Sobolev spaces without weights. Zbl 1205.35328 Krylov, N. V. 4 2009 First derivatives estimates for finite-difference schemes. Zbl 1198.65165 Gyöngy, István; Krylov, Nicolai 2 2009 Higher order derivative estimates for finite-difference schemes for linear elliptic and parabolic equations. Zbl 1183.65107 Gyöngy, István; Krylov, Nicolai 2 2009 Lectures on elliptic and parabolic equations in Sobolev spaces. Zbl 1147.35001 Krylov, N. V. 253 2008 On factorizations of smooth nonnegative matrix-values functions and on smooth functions with values in polyhedra. Zbl 1183.15011 Krylov, N. V. 10 2008 A brief overview of the \(L_p\)-theory of SPDEs. Zbl 1224.60161 Krylov, Nicolai 4 2008 Large deviations for occupation times of Markov processes with \(L_{2}\) semigroups. Zbl 1157.60022 Jain, Naresh; Krylov, Nicolai 4 2008 On parabolic PDEs and SPDEs in Sobolev spaces \(W^2_p\) without and with weights. Zbl 1152.60046 Krylov, Nicolai V. 3 2008 On the rate of convergence of the finite-difference approximations for parabolic Bellman equations with constant coefficients. Zbl 1166.49026 Luo, Jun; Krylov, N. V. 1 2008 Parabolic and elliptic equations with VMO coefficients. Zbl 1114.35079 Krylov, N. V. 176 2007 Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others. Zbl 1138.35308 Kim, Doyoon; Krylov, N. V. 77 2007 Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms. Zbl 1133.35052 Krylov, N. V. 72 2007 Parabolic equations with measurable coefficients. Zbl 1124.35024 Kim, Doyoon; Krylov, N. V. 59 2007 Stochastic evolution equations. Zbl 1130.60069 Krylov, Nicolai V.; Rozovskii, Boris L. 42 2007 The rate of convergence of finite-difference approximations for parabolic bellman equations with Lipschitz coefficients in cylindrical domains. Zbl 1127.65068 Dong, Hongjie; Krylov, Nicolai V. 24 2007 Maximum principle for SPDEs and its applications. Zbl 1135.60039 Krylov, Nicolai V. 18 2007 A priori estimates of smoothness of solutions to difference Bellman equations with linear and quasi-linear operators. Zbl 1112.65087 Krylov, N. V. 8 2007 On time-inhomogeneous controlled diffusion processes in domains. Zbl 1127.93062 Dong, Hongjie; Krylov, N. V. 6 2007 ...and 191 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,577 Authors 117 Krylov, Nicolaĭ Vladimirovich 84 Röckner, Michael 76 Dong, Hongjie 64 Shaposhnikov, Stanislav V. 60 Bogachev, Vladimir Igorevich 47 Kim, KyeongHun 44 Gyöngy, István 43 Flandoli, Franco 37 Zhang, Xicheng 34 Zheng, Shenzhou 29 Kim, Doyoon 28 Lions, Pierre-Louis 28 Wang, Feng-Yu 25 Pragarauskas, Henrikas 23 Byun, Sun-Sig 23 Mikulevicius, Remigijus 23 Veretennikov, Alexander Yu. 22 Kim, Ildoo 22 Luo, Dejun 21 Jentzen, Arnulf 21 Veraar, Mark C. 20 Phan, Tuoc Van 19 Priola, Enrico 18 Arapostathis, Aristotle 18 Barbu, Viorel 18 Da Prato, Giuseppe 18 Dareiotis, Konstantinos Anastasios 18 Hofmanová, Martina 18 Reisinger, Christoph 17 Feireisl, Eduard 17 Trudinger, Neil Sidney 17 Wei, Jinlong 16 Breit, Dominic 16 Brzeźniak, Zdzisław 16 Ivochkina, Nina Mikhaĭlovna 16 Jakobsen, Espen Robstad 16 Liu, Wei 15 Borkar, Vivek Shripad 15 Delarue, François 15 Huang, Xing 15 Kim, Seick 15 Qiu, Jinniao 15 Wang, Lihe 15 Wang, Xu-Jia 14 Bahlali, Khaled 14 Gess, Benjamin 14 Karlsen, Kenneth Hvistendahl 14 Lee, Kijung 14 Lorenzi, Luca 14 Menozzi, Stéphane 14 Proske, Frank Norbert 13 da Silva, João Vítor 13 Gerencsér, Máté 13 Pardoux, Etienne 13 Yi, Yingfei 13 Zhang, Junjie 12 Arkhipova, Arina Alekseevna 12 Biswas, Anup 12 Gao, Hongjun 12 Lieberman, Gary M. 12 Safonov, Mikhail V. 12 Scarpa, Luca 12 Šiška, David 12 Tang, Shanjian 11 Deugoue, Gabriel 11 Dokuchaev, Nikolai G. 11 Du, Kai 11 Freidlin, Mark I. 11 Hutzenthaler, Martin 11 Nualart, David 11 Peng, Shige 11 Pham, Huyên 11 Pimentel, Edgard A. 11 Rozovskii, Boris L. 11 Sango, Mamadou 11 Xie, Longjie 11 Zhang, Tusheng S. 10 Bao, Jiguang 10 Bayraktar, Erhan 10 Caffarelli, Luis Ángel 10 Cerrai, Sandra 10 Crisan, Dan O. 10 Debussche, Arnaud 10 Grothaus, Martin 10 Hu, Mingshang 10 Karatzas, Ioannis 10 Kinzebulatov, Damir 10 Lee, Ki-Ahm 10 Lee, Mikyoung 10 Marinelli, Carlo 10 Mishura, Yuliya Stepanivna 10 Mohan, Manil Thankamani 10 Nazarov, Alexander I. 10 Palagachev, Dian K. 10 Razafimandimby, Paul André 10 Russo, Francesco 10 Stannat, Wilhelm 10 Świȩch, Andrzej 10 Teixeira, Eduardo V. O. 10 Tian, Hong ...and 3,477 more Authors all top 5 Cited in 447 Serials 200 Journal of Differential Equations 187 Stochastic Processes and their Applications 141 Journal of Mathematical Analysis and Applications 116 Journal of Functional Analysis 87 Calculus of Variations and Partial Differential Equations 82 Stochastic and Partial Differential Equations. Analysis and Computations 73 Potential Analysis 72 Nonlinear Analysis. Theory, Methods & Applications. 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Serie IV 13 Journal of Economic Dynamics & Control 13 St. Petersburg Mathematical Journal 13 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 12 Ukrainian Mathematical Journal 12 Manuscripta Mathematica 12 Journal of Nonlinear Science 12 Comptes Rendus. Mathématique. Académie des Sciences, Paris 12 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 12 SIAM Journal on Financial Mathematics 12 Nonlinear Analysis. Theory, Methods & Applications 11 Theory of Probability and its Applications 11 Journal of Optimization Theory and Applications 11 Journal of Soviet Mathematics 11 Journal of Mathematical Fluid Mechanics 11 Communications in Contemporary Mathematics 10 Computers & Mathematics with Applications 10 Applied Mathematics and Computation 10 Inventiones Mathematicae 10 Chinese Annals of Mathematics. Series B 10 Physica D 10 Stochastics and Stochastics Reports 10 Boundary Value Problems 9 Journal of Mathematical Physics 9 Journal of Statistical Physics 9 Automatica 9 Journal of Applied Probability 9 Numerische Mathematik 9 European Journal of Operational Research 9 Theory of Probability and Mathematical Statistics 9 Electronic Communications in Probability 9 Advanced Nonlinear Studies 8 Applicable Analysis ...and 347 more Serials all top 5 Cited in 53 Fields 2,342 Partial differential equations (35-XX) 2,065 Probability theory and stochastic processes (60-XX) 451 Systems theory; control (93-XX) 387 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 385 Calculus of variations and optimal control; optimization (49-XX) 367 Numerical analysis (65-XX) 243 Fluid mechanics (76-XX) 222 Operator theory (47-XX) 209 Differential geometry (53-XX) 132 Functional analysis (46-XX) 131 Dynamical systems and ergodic theory (37-XX) 126 Ordinary differential equations (34-XX) 110 Global analysis, analysis on manifolds (58-XX) 108 Statistical mechanics, structure of matter (82-XX) 74 Operations research, mathematical programming (90-XX) 74 Biology and other natural sciences (92-XX) 70 Harmonic analysis on Euclidean spaces (42-XX) 60 Several complex variables and analytic spaces (32-XX) 59 Integral equations (45-XX) 57 Real functions (26-XX) 55 Statistics (62-XX) 47 Potential theory (31-XX) 37 Convex and discrete geometry (52-XX) 30 Mechanics of deformable solids (74-XX) 25 Measure and integration (28-XX) 25 Mechanics of particles and systems (70-XX) 23 Difference and functional equations (39-XX) 23 Computer science (68-XX) 23 Classical thermodynamics, heat transfer (80-XX) 18 Quantum theory (81-XX) 18 Geophysics (86-XX) 13 History and biography (01-XX) 12 Approximations and expansions (41-XX) 10 Functions of a complex variable (30-XX) 7 Algebraic geometry (14-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 6 Optics, electromagnetic theory (78-XX) 6 Information and communication theory, circuits (94-XX) 5 General and overarching topics; collections (00-XX) 5 Topological groups, Lie groups (22-XX) 5 Abstract harmonic analysis (43-XX) 5 Integral transforms, operational calculus (44-XX) 4 Combinatorics (05-XX) 4 Nonassociative rings and algebras (17-XX) 3 Special functions (33-XX) 2 Mathematical logic and foundations (03-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 2 Relativity and gravitational theory (83-XX) 2 Astronomy and astrophysics (85-XX) 1 Associative rings and algebras (16-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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