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 Author ID: krylov.nicolai-v Published as: Krylov, N.; Krylov, N. V.; Krylov, Nicolai; Krylov, Nicolai V.; Krylov, Nicolaï Homepage: http://www.math.umn.edu/~nkrylov/ External Links: MGP · Math-Net.Ru · Wikidata · ResearchGate · dblp · GND
 Documents Indexed: 317 Publications since 1964, including 19 Books Biographic References: 1 Publication
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#### Co-Authors

 220 single-authored 22 Gyöngy, István 13 Rozovskii, Boris L. 10 Röckner, Michael 8 Bogachev, Vladimir Igorevich 8 Dong, Hongjie 6 Safonov, Mikhail V. 4 Liptser, Robert 4 Veretennikov, Alexander Yu. 3 Genis, I. L. 3 Priola, Enrico 3 Shiryaev, Al’bert Nikolaevich 3 Yushkevich, Aleksandr Adol’fovich 2 Anulova, Svetlana 2 Jain, Naresh C. 2 Khas’minskiĭ, Rafail Zalmanovich 2 Kim, Doyoon 2 Kim, KyeongHun 2 Lototsky, Sergey V. 2 Miroshnichenko, Taisia P. 2 Nosovskij, G. V. 2 Novikov, Aleksandr Aleksandrovich 2 Pragarauskas, G. 2 Zatezalo, Aleksandar 1 Alyushina, L. A. 1 Boccia, Serafino 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 Wang, Teng 1 Yastrzhembskiy, Timur 1 Zabczyk, Jerzy 1 Zvonkin, Alexander K.
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#### Serials

 16 Mathematics of the USSR. Izvestiya 15 Theory of Probability and its Applications 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 10 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 9 Applied Mathematics and Optimization 9 Stochastic Processes and their Applications 8 Teoriya Veroyatnosteĭ i eë Primeneniya 7 Soviet Mathematics. Doklady 7 St. Petersburg Mathematical Journal 6 The Annals of Probability 6 Journal of Functional Analysis 4 Mathematics of Computation 4 Siberian Mathematical Journal 4 Sibirskiĭ Matematicheskiĭ Zhurnal 4 Journal of Mathematical Sciences (New York) 4 Methods and Applications of Analysis 3 Lithuanian Mathematical Journal 3 Uspekhi Matematicheskikh Nauk [N. S.] 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Transactions of the American Mathematical Society 3 Stochastics and Stochastics Reports 3 Potential Analysis 3 Electronic Journal of Probability 3 Graduate Studies in Mathematics 2 Mathematical Notes 2 Russian Mathematical Surveys 2 Stochastics 2 Ukraïns’kyĭ Matematychnyĭ Zhurnal 2 Differentsial’nye Uravneniya 2 Differential Equations 2 Illinois Journal of Mathematics 2 Journal of Soviet Mathematics 2 Differential and Integral Equations 2 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 2 Topological Methods in Nonlinear Analysis 2 Calculus of Variations and Partial Differential Equations 2 Doklady Mathematics 2 Mathematical Surveys and Monographs 2 Stochastic and Partial Differential Equations. Analysis and Computations 2 Applications of Mathematics 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Matematicheskie Zametki 1 Moscow University Mathematics Bulletin 1 Ukrainian Mathematical Journal 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 Journal of Dynamics and Differential Equations 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 NoDEA. Nonlinear Differential Equations and Applications 1 Journal of Convex Analysis 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 Complex Variables and Elliptic Equations 1 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya 1 Lecture Notes in Mathematics 1 Translations of Mathematical Monographs 1 Student Mathematical Library 1 Analysis and Mathematical Physics
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#### Fields

 170 Partial differential equations (35-XX) 170 Probability theory and stochastic processes (60-XX) 50 Systems theory; control (93-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 24 Numerical analysis (65-XX) 9 Statistics (62-XX) 7 Difference and functional equations (39-XX) 7 Functional analysis (46-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Operator theory (47-XX) 5 Operations research, mathematical programming (90-XX) 4 Real functions (26-XX) 4 Ordinary differential equations (34-XX) 3 General and overarching topics; collections (00-XX) 3 Measure and integration (28-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Convex and discrete geometry (52-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

252 Publications have been cited 4,203 times in 2,522 Documents Cited by Year
Controlled diffusion processes. Transl. by A. B. Aries. Zbl 0459.93002
Krylov, N. V.
1980
Nonlinear elliptic and parabolic equations of the second order. Transl. from the Russian by P. L. Buzytsky. Zbl 0619.35004
Krylov, N. V.
1987
Lectures on elliptic and parabolic equations in Hölder spaces. Zbl 0865.35001
Krylov, N. V.
1996
Existence of strong solutions for Itô’s stochastic equations via approximations. Zbl 0847.60038
Gyöngy, István; Krylov, Nicolai
1996
Strong solutions of stochastic equations with singular time dependent drift. Zbl 1072.60050
Krylov, N. V.; Röckner, M.
2005
Lectures on elliptic and parabolic equations in Sobolev spaces. Zbl 1147.35001
Krylov, N. V.
2008
An analytic approach to SPDEs. Zbl 0933.60073
Krylov, N. V.
1999
Parabolic and elliptic equations with VMO coefficients. Zbl 1114.35079
Krylov, N. V.
2007
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.
2001
Stochastic evolution equations. Zbl 0462.60060
Krylov, N. V.; Rozovskij, B. L.
1981
Some new results in the theory of controlled diffusion processes. Zbl 0436.93055
Krylov, N. V.
1980
Bounded inhomogeneous elliptic and parabolic equations. Zbl 0511.35002
Krylov, N. V.
1982
A certain property of solutions of parabolic equations with measurable coefficients. Zbl 0464.35035
Krylov, N. V.; Safonov, M. V.
1981
Nonlinear elliptic and parabolic equations of second order. Zbl 0586.35002
Krylov, N. V.
1985
Controlled processes of diffusion type. Zbl 0513.60043
Krylov, N. V.
1977
An estimate of the probability that a diffusion process hits a set of positive measure. Zbl 0459.60067
Krylov, N. V.; Safonov, M. V.
1979
On the rate of convergence of finite-difference approximations for Bellman’s equations with variable coefficients. Zbl 0971.65081
Krylov, N. V.
2000
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.
2007
Introduction to the theory of diffusion processes. Transl. from the Russian by V. Khidekel a. G. Pasechnik. Zbl 0844.60050
Krylov, N. V.
1995
Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms. Zbl 1133.35052
Krylov, N. V.
2007
Elliptic and parabolic equations for measures. Zbl 1194.35481
Bogachev, V. I.; Krylov, N. V.; Röckner, M.
2009
Fokker-Planck-Kolmogorov equations. Zbl 1342.35002
Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael; Shaposhnikov, Stanislav V.
2015
On the Cauchy problem for linear stochastic partial differential equations. Zbl 0396.60058
Krylov, N. V.; Rozovskii, B. L.
1977
On stochastics equations with respect to semimartingales. II. Ito formula in Banach spaces. Zbl 0481.60060
Gyoengy, I.; Krylov, N. V.
1982
On $$L_ p$$-theory of stochastic partial differential equations in the whole space. Zbl 0846.60061
Krylov, N. V.
1996
On stochastic equations with respect to semimartingales I. Zbl 0439.60061
Gyöngy, I.; Krylov, N. V.
1980
A $$W_ 2^ n$$-theory of the Dirichlet problem for SPDEs in general smooth domains. Zbl 0794.60062
Krylov, N. V.
1994
Parabolic equations with measurable coefficients. Zbl 1124.35024
Kim, Doyoon; Krylov, N. V.
2007
Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation. Zbl 0362.35038
Krylov, N. V.
1976
Second-order elliptic equations with variably partially VMO coefficients. Zbl 1171.35352
Krylov, N. V.
2009
Boundedly nonhomogeneous elliptic and parabolic equations. Zbl 0529.35026
Krylov, N. V.
1983
A Sobolev space theory of SPDEs with constant coefficients in a half space. Zbl 0943.60047
Krylov, N. V.; Lototsky, S. V.
1999
Boundedly nonhomogeneous elliptic and parabolic equations in a domain. Zbl 0578.35024
Krylov, N. V.
1984
The rate of convergence of finite-difference approximations for Bellman equations with Lipschitz coefficients. Zbl 1087.65100
Krylov, Nicolai V.
2005
On the Itô–Wentzell formula for distribution-valued processes and related topics. Zbl 1238.60060
Krylov, N. V.
2011
On the general notion of fully nonlinear second-order elliptic equations. Zbl 0832.35042
Krylov, N. V.
1995
On the splitting-up method and stochastic partial differential equations. Zbl 1028.60058
Gyöngy, István; Krylov, Nicolai
2003
Some properties of traces for stochastic and deterministic parabolic weighted Sobolev spaces. Zbl 0980.60091
Krylov, N. V.
2001
Controlled diffusion processes. Translated by A. B. Aries. Reprint of the 1980 ed. Zbl 1171.93004
Krylov, N. V.
2009
On the Sobolev space theory of parabolic and elliptic equations in $$C^{1}$$ domains. Zbl 1083.35041
Kim, Kyeong-Hun; Krylov, N. V.
2004
Weighted Sobolev spaces and Laplace’s equation and the heat equations in a half space. Zbl 0934.35032
Krylov, N. V.
1999
Elliptic and parabolic second-order PDEs with growing coefficients. Zbl 1195.35160
Krylov, N. V.; Priola, E.
2010
The heat equation in $$L_{q}((0,T),L_{p})$$-spaces with weights. Zbl 0979.35060
Krylov, N. V.
2001
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.
1974
On Ito’s stochastic integral equations. Zbl 0281.60066
Krylov, N. V.
1969
Approximating value functions for controlled degenerate diffusion processes by using piece-wise constant policies. Zbl 1044.93546
Krylov, N. V.
1999
Control of a solution of a stochastic integral equation. Zbl 0265.60055
Krylov, N. V.
1972
On weak uniqueness for some diffusions with discontinuous coefficients. Zbl 1073.60064
Krylov, N. V.
2004
A Sobolev space theory of SPDE with constant coefficients on a half line. Zbl 0928.60042
Krylov, N. V.; Lototsky, S. V.
1999
Itô’s formula for the $$L _{p }$$-norm of stochastic $${W^{1}_{p}}$$-valued processes. Zbl 1232.60050
Krylov, N. V.
2010
Elliptic regularity and essential self-adjointness of Dirichlet operators on $$\mathbb{R}^n$$. Zbl 0901.35017
Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael
1997
Stochastic evolution equations. Zbl 1130.60069
Krylov, Nicolai V.; Rozovskii, Boris L.
2007
A generalization of the Littlewood-Paley inequality and some other results related to stochastic partial differential equations. Zbl 0870.42005
Krylov, N. V.
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.
2007
A simple proof of the existence of a solution of Itô’s equation with monotone coefficients. Zbl 0735.60061
Krylov, N. V.
1990
On averaging principle for diffusion processes with null-recurrent fast component. Zbl 1053.60060
Khasminskii, R.; Krylov, N.
2001
A relatively short proof of Itô’s formula for SPDEs and its applications. Zbl 1274.60204
Krylov, N. V.
2013
Accelerated finite difference schemes for linear stochastic partial differential equations in the whole space. Zbl 1222.65009
Gyöngy, István; Krylov, Nicolai
2010
On the rate of convergence of splitting-up approximations for SPDEs. Zbl 1038.60057
Gyöngy, István; Krylov, Nicolai
2003
Regularity of invariant measures: The case of non-constant diffusion part. Zbl 0929.60039
Bogachev, V. I.; Krylov, N.; Röckner, M.
1996
On degenerate nonlinear elliptic equations. Zbl 0525.35038
Krylov, N. V.
1983
Stochastic partial differential equations and diffusion processes. Zbl 0518.60072
Krylov, N. V.; Rozovskij, B. L.
1982
An inequality in the theory of stochastic integrals. Zbl 0238.60038
Krylov, N. V.
1971
Second-order elliptic and parabolic equations with $$B(\mathbb R^2, \mathrm{VMO})$$ coefficients. Zbl 1207.35174
Dong, Hongjie; Krylov, N. V.
2010
On conditional distributions of diffusion processes. Zbl 0402.60077
Krylov, N. V.; Rozovskii, B. L.
1978
Fully nonlinear second order elliptic equations: recent development. Zbl 1033.35036
Krylov, Nicolai V.
1997
Elliptic equations for measures: regularity and global bounds of densities. Zbl 1206.35242
Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael
2006
Maximum principle for SPDEs and its applications. Zbl 1135.60039
Krylov, Nicolai V.
2007
Introduction to the theory of random processes. Zbl 1008.60001
Krylov, N. V.
2002
Characteristics of degenerate second-order parabolic Ito equations. Zbl 0584.60068
Krylov, N. V.; Rozovskij, B. L.
1986
On characteristics of the degenerate second order Ito parabolic equations. Zbl 0503.60066
Krylov, N. V.; Rozovskij, B. L.
1982
On the existence of $$W^2_p$$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions. Zbl 1277.35172
Krylov, N. V.
2013
On Kolmogorov’s equations for finite dimensional diffusions. Zbl 0943.60070
Krylov, N. V.
1999
Smoothness of the value function for a controlled diffusion process in a domain. Zbl 0701.93054
Krylov, N. V.
1990
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.
1987
On controlled diffusion processes with unbounded coefficients. Zbl 0514.93070
Krylov, N. V.
1982
Some $$L_{p}$$-estimates for elliptic and parabolic operators with measurable coefficients. Zbl 1258.35069
Krylov, N. V.
2012
On factorizations of smooth nonnegative matrix-values functions and on smooth functions with values in polyhedra. Zbl 1183.15011
Krylov, N. V.
2008
On SPDEs with variable coefficients in one space dimension. Zbl 1059.60075
Kim, Kyeong-Hun; Krylov, N. V.
2004
Some properties of weighted Sobolev spaces in $$\mathbb{R}_+^d$$. Zbl 0962.46016
Krylov, Nicolai V.
1999
On the rate of convergence of finite-difference approximations for Bellman’s equations. Zbl 0902.65035
Krylov, N. V.
1997
Stochastic partial differential equations and diffusion processes. Zbl 0508.60054
Krylov, N. V.; Rozovskij, B. L.
1982
On controlled diffusion processes with unbounded coefficients. Zbl 0497.93060
Krylov, N. V.
1981
On the first integrals and Liouville equations for diffusion processes. Zbl 0474.60049
Krylov, N. V.; Rozovskii, B. L.
1981
Explicit formulae for the solutions of stochastic equations. Zbl 0353.60059
Veretennikov, A. Yu.; Krylov, N. V.
1976
On strong solutions of stochastic differential equations. Zbl 0481.60062
Zvonkin, A. K.; Krylov, N. V.
1975
On the rate of convergence of finite-difference approximations for elliptic Isaacs equations in smooth domains. Zbl 1331.65122
Krylov, N. V.
2015
On the foundation of the $$L_p$$-theory of stochastic partial differential equations. Zbl 1165.60331
Krylov, Nicolai V.
2006
An accelerated splitting-up method for parabolic equations. Zbl 1101.35038
Gyöngy, István; Krylov, Nicolai
2005
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.
2005
SPDEs in $$L_q(\mskip-2mu(0,\tau], L_p)$$ spaces. Zbl 0963.60053
Krylov, N. V.
2000
On Itô stochastic integral equations. Zbl 0214.44301
Krylov, N. V.
1969
On the solvability of degenerate stochastic partial differential equations in Sobolev spaces. Zbl 1310.60094
Gerencsér, Máté; Gyöngy, István; Krylov, Nicolai
2015
On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains and the Isaacs equations. Zbl 1290.91022
Krylov, N. V.
2014
On the existence of smooth solutions for fully nonlinear elliptic equations with measurable “coefficients” without convexity assumptions. Zbl 1285.35033
Krylov, Nicolai V.
2012
A priori estimates of smoothness of solutions to difference Bellman equations with linear and quasi-linear operators. Zbl 1112.65087
Krylov, N. V.
2007
On the rate of convergence of finite-difference approximations for Bellman equations with constant coefficients. Zbl 1136.49312
Dong, Hongjie; Krylov, N. V.
2006
Parabolic equations in $$L_p$$-spaces with mixed norms. Zbl 1032.35046
Krylov, N. V.
2003
On the Calderón-Zygmund theorem with applications to parabolic equations. Zbl 1011.35033
Krylov, N. V.
2002
A parabolic Littlewood-Paley inequality with applications to parabolic equations. Zbl 0839.35017
Krylov, N. V.
1994
On Shige Peng’s central limit theorem. Zbl 1433.60013
Krylov, N. V.
2020
Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces. Zbl 1418.35211
Dong, Hongjie; Krylov, N. V.
2019
Sobolev and viscosity solutions for fully nonlinear elliptic and parabolic equations. Zbl 1401.35001
Krylov, N. V.
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.
2018
$$C^{1+\alpha}$$-regularity of viscosity solutions of general nonlinear parabolic equations. Zbl 1402.35061
Krylov, N. V.
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.
2017
Poisson stochastic process and basic Schauder and Sobolev estimates in the theory of parabolic equations. Zbl 1375.35551
Krylov, N. V.; Priola, Enrico
2017
On nonequivalence of regular boundary points for second-order elliptic operators. Zbl 1379.35099
Krylov, N. V.; Yastrzhembskiy, Timur
2017
On parabolic equations in one space dimension. Zbl 1346.35081
Krylov, N. V.
2016
Hörmander’s theorem for stochastic partial differential equations. Zbl 1439.60061
Krylov, N. V.
2016
Fokker-Planck-Kolmogorov equations. Zbl 1342.35002
Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael; Shaposhnikov, Stanislav V.
2015
On the rate of convergence of finite-difference approximations for elliptic Isaacs equations in smooth domains. Zbl 1331.65122
Krylov, N. V.
2015
On the solvability of degenerate stochastic partial differential equations in Sobolev spaces. Zbl 1310.60094
Gerencsér, Máté; Gyöngy, István; Krylov, Nicolai
2015
To the theory of viscosity solutions for uniformly parabolic Isaacs equations. Zbl 1329.35170
Krylov, N. V.
2015
Hypoellipticity for filtering problems of partially observable diffusion processes. Zbl 1317.60098
Krylov, N. V.
2015
Approximating the value functions for stochastic differential games with the ones having bounded second derivatives. Zbl 1302.49053
Krylov, N. V.
2015
On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains and the Isaacs equations. Zbl 1290.91022
Krylov, N. V.
2014
On the rate of convergence of difference approximations for uniformly nondegenerate elliptic Bellman’s equations. Zbl 1297.65073
Krylov, N. V.
2014
On $$C^{1+\alpha}$$ regularity of solutions of Isaacs parabolic equations with VMO coefficients. Zbl 1304.35173
Krylov, N. V.
2014
On regularity properties and approximations of value functions for stochastic differential games in domains. Zbl 1336.91020
Krylov, N. V.
2014
Hörmander’s theorem for parabolic equations with coefficients measurable in the time variable. Zbl 1288.35315
Krylov, N. V.
2014
To the theory of viscosity solutions for uniformly elliptic Isaacs equations. Zbl 1302.35171
Krylov, N. V.
2014
On the independence of the value function for stochastic differential games of the probability space. Zbl 1307.91033
Krylov, N. V.
2014
On the fundamental matrix solution for higher-order parabolic systems. Zbl 1319.35075
Boccia, S.; Krylov, N. V.
2014
A relatively short proof of Itô’s formula for SPDEs and its applications. Zbl 1274.60204
Krylov, N. V.
2013
On the existence of $$W^2_p$$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions. Zbl 1277.35172
Krylov, N. V.
2013
On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains. Zbl 1287.49027
Krylov, N. V.
2013
On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains. Zbl 1278.35133
Dong, Hongjie; Krylov, N. V.; Li, Xu
2013
An ersatz existence theorem for fully nonlinear parabolic equations without convexity assumptions. Zbl 1295.35262
Krylov, N. V.
2013
On the existence of smooth solutions for fully nonlinear parabolic equations with measurable “coefficients” without convexity assumptions. Zbl 06190731
Dong, Hongjie; Krylov, N. V.
2013
Interior estimates for second-order differences of solutions of finite-difference elliptic Bellman’s equations. Zbl 1269.49050
Krylov, N. V.
2013
Some $$L_{p}$$-estimates for elliptic and parabolic operators with measurable coefficients. Zbl 1258.35069
Krylov, N. V.
2012
On the existence of smooth solutions for fully nonlinear elliptic equations with measurable “coefficients” without convexity assumptions. Zbl 1285.35033
Krylov, Nicolai V.
2012
Interior estimates for the first-order differences for finite-difference approximations for elliptic Bellman’s equations. Zbl 1244.49053
Krylov, N. V.
2012
On the Itô–Wentzell formula for distribution-valued processes and related topics. Zbl 1238.60060
Krylov, N. V.
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.
2011
Accelerated finite difference schemes for second order degenerate elliptic and parabolic problems in the whole space. Zbl 1223.65068
Gyöngy, István; Krylov, Nicolai
2011
Filtering partially observable diffusions up to the exit time from a domain. Zbl 1233.62168
Krylov, N. V.; Wang, Teng
2011
Filtering equations for partially observable diffusion processes with Lipschitz continuous coefficients. Zbl 1223.93112
Krylov, N. V.
2011
On divergence form second-order PDEs with growing coefficients in $$W^{1}_{p}$$ spaces without weights. Zbl 1254.35108
Krylov, N. V.
2011
Accelerated numerical schemes for PDEs and SPDEs. Zbl 1221.65222
Gyöngy, István; Krylov, Nicolai
2011
Elliptic and parabolic second-order PDEs with growing coefficients. Zbl 1195.35160
Krylov, N. V.; Priola, E.
2010
Itô’s formula for the $$L _{p }$$-norm of stochastic $${W^{1}_{p}}$$-valued processes. Zbl 1232.60050
Krylov, N. V.
2010
Accelerated finite difference schemes for linear stochastic partial differential equations in the whole space. Zbl 1222.65009
Gyöngy, István; Krylov, Nicolai
2010
Second-order elliptic and parabolic equations with $$B(\mathbb R^2, \mathrm{VMO})$$ coefficients. Zbl 1207.35174
Dong, Hongjie; Krylov, N. V.
2010
On Bellman’s equations with VMO coefficients. Zbl 1208.35052
Krylov, Nicolai V.
2010
About an example of N. N, Ural’tseva and weak uniqueness for elliptic operators. Zbl 1387.35149
Krylov, N. V.
2010
On divergence form SPDEs with growing coefficients in $$W^{1}_{2}$$ spaces without weights. Zbl 1218.60057
Krylov, N. V.
2010
Elliptic and parabolic equations for measures. Zbl 1194.35481
Bogachev, V. I.; Krylov, N. V.; Röckner, M.
2009
Second-order elliptic equations with variably partially VMO coefficients. Zbl 1171.35352
Krylov, N. V.
2009
Controlled diffusion processes. Translated by A. B. Aries. Reprint of the 1980 ed. Zbl 1171.93004
Krylov, N. V.
2009
On divergence form SPDEs with VMO coefficients. Zbl 1195.60091
Krylov, N. V.
2009
On divergence form SPDEs with VMO coefficients in a half space. Zbl 1165.60330
Krylov, N. V.
2009
On linear elliptic and parabolic equations with growing drift in Sobolev spaces without weights. Zbl 1205.35328
Krylov, N. V.
2009
First derivatives estimates for finite-difference schemes. Zbl 1198.65165
Gyöngy, István; Krylov, Nicolai
2009
Higher order derivative estimates for finite-difference schemes for linear elliptic and parabolic equations. Zbl 1183.65107
Gyöngy, István; Krylov, Nicolai
2009
Lectures on elliptic and parabolic equations in Sobolev spaces. Zbl 1147.35001
Krylov, N. V.
2008
On factorizations of smooth nonnegative matrix-values functions and on smooth functions with values in polyhedra. Zbl 1183.15011
Krylov, N. V.
2008
Large deviations for occupation times of Markov processes with $$L_{2}$$ semigroups. Zbl 1157.60022
Jain, Naresh; Krylov, Nicolai
2008
A brief overview of the $$L_p$$-theory of SPDEs. Zbl 1224.60161
Krylov, Nicolai
2008
On parabolic PDEs and SPDEs in Sobolev spaces $$W^2_p$$ without and with weights. Zbl 1152.60046
Krylov, Nicolai V.
2008
Parabolic and elliptic equations with VMO coefficients. Zbl 1114.35079
Krylov, N. V.
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.
2007
Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms. Zbl 1133.35052
Krylov, N. V.
2007
Parabolic equations with measurable coefficients. Zbl 1124.35024
Kim, Doyoon; Krylov, N. V.
2007
Stochastic evolution equations. Zbl 1130.60069
Krylov, Nicolai V.; Rozovskii, Boris L.
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.
2007
Maximum principle for SPDEs and its applications. Zbl 1135.60039
Krylov, Nicolai V.
2007
A priori estimates of smoothness of solutions to difference Bellman equations with linear and quasi-linear operators. Zbl 1112.65087
Krylov, N. V.
2007
On time-inhomogeneous controlled diffusion processes in domains. Zbl 1127.93062
Dong, Hongjie; Krylov, N. V.
2007
Filtering and prediction: A primer. Zbl 1165.62070
Fristedt, B.; Jain, N.; Krylov, N.
2007
Elliptic equations for measures: regularity and global bounds of densities. Zbl 1206.35242
Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael
2006
On the foundation of the $$L_p$$-theory of stochastic partial differential equations. Zbl 1165.60331
Krylov, Nicolai V.
2006
On the rate of convergence of finite-difference approximations for Bellman equations with constant coefficients. Zbl 1136.49312
Dong, Hongjie; Krylov, N. V.
2006
Expansion of solutions of parameterized equations and acceleration of numerical methods. Zbl 1123.65084
Gyöngy, István; Krylov, Nicolai
2006
Strong solutions of stochastic equations with singular time dependent drift. Zbl 1072.60050
Krylov, N. V.; Röckner, M.
2005
The rate of convergence of finite-difference approximations for Bellman equations with Lipschitz coefficients. Zbl 1087.65100
Krylov, Nicolai V.
2005
An accelerated splitting-up method for parabolic equations. Zbl 1101.35038
Gyöngy, István; Krylov, Nicolai
2005
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.
2005
Regularity and global bounds of densities of invariant measures of diffusion processes. Zbl 1131.60072
Bogachev, V. I.; Krylov, N. V.; Röckner, M.
2005
On the Sobolev space theory of parabolic and elliptic equations in $$C^{1}$$ domains. Zbl 1083.35041
Kim, Kyeong-Hun; Krylov, N. V.
2004
On weak uniqueness for some diffusions with discontinuous coefficients. Zbl 1073.60064
Krylov, N. V.
2004
On SPDEs with variable coefficients in one space dimension. Zbl 1059.60075
Kim, Kyeong-Hun; Krylov, N. V.
2004
Probabilistic methods of investigating interior smoothness of harmonic functions associated with degenerate elliptic operators. Zbl 1130.60300
Krylov, Nicolai V.
2004
Quasiderivatives and interior smoothness of harmonic functions associated with degenerate diffusion processes. Zbl 1064.60172
Krylov, N. V.
2004
On the splitting-up method and stochastic partial differential equations. Zbl 1028.60058
Gyöngy, István; Krylov, Nicolai
2003
On the rate of convergence of splitting-up approximations for SPDEs. Zbl 1038.60057
Gyöngy, István; Krylov, Nicolai
2003
Parabolic equations in $$L_p$$-spaces with mixed norms. Zbl 1032.35046
Krylov, N. V.
2003
Brownian trajectory is a regular lateral boundary for the heat equation. Zbl 1028.60039
Krylov, N. V.
2003
On more square root law for Brownian motion and its application to SPDEs. Zbl 1048.60031
Krylov, N. V.
2003
Introduction to the theory of random processes. Zbl 1008.60001
Krylov, N. V.
2002
On the Calderón-Zygmund theorem with applications to parabolic equations. Zbl 1011.35033
Krylov, N. V.
2002
The Calder’on-Zygmund theorem and parabolic equations in $$L_p(\mathbb R, C^{2+\alpha})$$-spaces. Zbl 1170.35434
Krylov, Nicolai V.
2002
On diffusion approximation with discountinuous coefficients. Zbl 1075.60558
Krylov, N. V.; Liptser, R.
2002
Adapting some ideas from stochastic control theory to studying the heat equation in closed smooth domains. Zbl 1030.35093
Krylov, Nicolai V.
2002
A supermartingale characterization of sets of stochastic integrals and applications. Zbl 1009.60038
Krylov, N. V.
2002
Some new results in the theory of SPDEs in Sobolev spaces. Zbl 1001.60069
Krylov, N. V.
2002
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.
2001
Some properties of traces for stochastic and deterministic parabolic weighted Sobolev spaces. Zbl 0980.60091
Krylov, N. V.
2001
The heat equation in $$L_{q}((0,T),L_{p})$$-spaces with weights. Zbl 0979.35060
Krylov, N. V.
2001
...and 152 more Documents
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#### Cited by 2,319 Authors

 88 Krylov, Nicolaĭ Vladimirovich 62 Röckner, Michael 48 Shaposhnikov, Stanislav V. 44 Bogachev, Vladimir Igorevich 40 Dong, Hongjie 38 Kim, KyeongHun 37 Gyöngy, István 30 Flandoli, Franco 26 Lions, Pierre-Louis 24 Zhang, Xicheng 21 Kim, Doyoon 20 Mikulevicius, Remigijus 20 Zheng, Shenzhou 19 Byun, Sun-Sig 18 Da Prato, Giuseppe 18 Kim, Ildoo 17 Trudinger, Neil Sidney 17 Wang, Feng-Yu 16 Barbu, Viorel 15 Wang, Xu-Jia 14 Lorenzi, Luca 14 Pragarauskas, Henrikas 14 Priola, Enrico 14 Veretennikov, Alexander Yu. 13 Dareiotis, Konstantinos Anastasios 13 Jakobsen, Espen Robstad 13 Pardoux, Etienne 13 Wang, Lihe 13 Yi, Yingfei 12 Ivochkina, Nina Mikhaĭlovna 12 Jentzen, Arnulf 12 Veraar, Mark C. 11 Freidlin, Mark I. 11 Lee, Kijung 11 Luo, Dejun 11 Nualart, David 11 Phan, Tuoc Van 11 Pragarauskas, G. 10 Arapostathis, Aristotle 10 Bahlali, Khaled 10 Borkar, Vivek Shripad 10 Brzeźniak, Zdzisław 10 Du, Kai 10 Karlsen, Kenneth Hvistendahl 10 Lieberman, Gary M. 10 Matoussi, Anis 10 Pham, Huyên 10 Proske, Frank Norbert 10 Rozovskii, Boris L. 10 Sango, Mamadou 9 Biswas, Anup 9 Cerrai, Sandra 9 Delarue, François 9 Deugoue, Gabriel 9 Dokuchaev, Nikolai G. 9 Gess, Benjamin 9 Hofmanová, Martina 9 Ji, Min 9 Karatzas, Ioannis 9 Mishura, Yuliya Stepanivna 9 Nazarov, Alexander I. 9 Razafimandimby, Paul André 9 Reisinger, Christoph 9 Safonov, Mikhail V. 9 Sirakov, Boyan Slavchev 9 Zhang, Tusheng S. 8 Arkhipova, Arina A. Arkhipova 8 Bensoussan, Alain 8 Caffarelli, Luis Ángel 8 Debussche, Arnaud 8 Feehan, Paul M. N. 8 Gerencsér, Máté 8 Goreac, Dan 8 Kim, Seick 8 Kloeden, Peter Eris 8 Kulinich, Grygoriĭ L. 8 Ouknine, Youssef 8 Pop, Camelia Alexandra 8 Świȩch, Andrzej 8 Tang, Shanjian 8 Temam, Roger Meyer 8 Touzi, Nizar 8 Xie, Longjie 8 Xiong, Jie 8 Yao, Fengping 8 Zhang, Junjie 7 Bao, Jiguang 7 Bayraktar, Erhan 7 Breit, Dominic 7 Grothaus, Martin 7 Huang, Xing 7 Levakov, Anatoliĭ Afanas’evich 7 Manita, Oxana A. 7 Marinelli, Carlo 7 Palagachev, Dian K. 7 Peng, Shige 7 Qiu, Jinniao 7 Russo, Francesco 7 Ryu, Seungjin 7 Shen, Zhongwei ...and 2,219 more Authors
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#### Cited in 335 Serials

 145 Stochastic Processes and their Applications 133 Journal of Differential Equations 97 Journal of Mathematical Analysis and Applications 86 Journal of Functional Analysis 54 The Annals of Probability 51 Probability Theory and Related Fields 51 Communications in Partial Differential Equations 51 Potential Analysis 47 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 47 Calculus of Variations and Partial Differential Equations 47 Journal of Mathematical Sciences (New York) 46 Transactions of the American Mathematical Society 44 Applied Mathematics and Optimization 41 Stochastic Analysis and Applications 38 Stochastic and Partial Differential Equations. Analysis and Computations 37 The Annals of Applied Probability 36 SIAM Journal on Control and Optimization 32 Archive for Rational Mechanics and Analysis 32 Doklady Mathematics 31 Journal de Mathématiques Pures et Appliquées. Neuvième Série 30 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 28 Stochastics and Dynamics 27 Advances in Mathematics 26 SIAM Journal on Mathematical Analysis 25 Discrete and Continuous Dynamical Systems 23 Lithuanian Mathematical Journal 23 Stochastics 23 Journal of Theoretical Probability 21 NoDEA. Nonlinear Differential Equations and Applications 20 Journal of Evolution Equations 19 Proceedings of the American Mathematical Society 19 Communications on Pure and Applied Analysis 18 Systems & Control Letters 18 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 17 Mathematische Annalen 16 Acta Applicandae Mathematicae 16 Differential Equations 16 Stochastics 15 Mathematics of Computation 15 Mathematical Finance 14 Journal of Computational and Applied Mathematics 14 Mathematische Zeitschrift 14 The Journal of Geometric Analysis 13 Mathematical Notes 13 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 13 Siberian Mathematical Journal 13 Statistics & Probability Letters 13 Discrete and Continuous Dynamical Systems. Series B 12 Communications in Mathematical Physics 12 SIAM Journal on Numerical Analysis 12 Journal of Economic Dynamics & Control 12 Bulletin des Sciences Mathématiques 12 Finance and Stochastics 12 Nonlinear Analysis. Real World Applications 12 Comptes Rendus. Mathématique. Académie des Sciences, Paris 12 Nonlinear Analysis. Theory, Methods & Applications 11 Journal of Soviet Mathematics 11 Infinite Dimensional Analysis, Quantum Probability and Related Topics 11 Acta Mathematica Sinica. English Series 11 Science China. Mathematics 10 Duke Mathematical Journal 10 Journal für die Reine und Angewandte Mathematik 10 Stochastics and Stochastics Reports 9 Computers & Mathematics with Applications 9 Communications on Pure and Applied Mathematics 9 Ukrainian Mathematical Journal 9 Annali di Matematica Pura ed Applicata. Serie Quarta 9 Manuscripta Mathematica 9 Chinese Annals of Mathematics. Series B 9 Journal of Dynamics and Differential Equations 9 Journal of Nonlinear Science 9 St. Petersburg Mathematical Journal 8 Automatica 8 Electronic Journal of Probability 7 Annales de l’Institut Fourier 7 Applied Mathematics and Computation 7 Inventiones Mathematicae 7 Journal of Optimization Theory and Applications 7 European Journal of Operational Research 7 Bernoulli 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 7 Communications in Contemporary Mathematics 7 SIAM Journal on Financial Mathematics 6 Journal of Mathematical Physics 6 Nonlinearity 6 Acta Mathematica 6 Journal of Applied Probability 6 Numerische Mathematik 6 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 6 Insurance Mathematics & Economics 6 Acta Mathematicae Applicatae Sinica. English Series 6 Journal of Scientific Computing 6 Bulletin of the American Mathematical Society. New Series 6 Abstract and Applied Analysis 6 Boundary Value Problems 6 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Mathematical Control and Related Fields 5 International Journal of Control 5 Journal of Applied Mathematics and Mechanics 5 Journal of Statistical Physics ...and 235 more Serials
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#### Cited in 48 Fields

 1,407 Partial differential equations (35-XX) 1,330 Probability theory and stochastic processes (60-XX) 334 Systems theory; control (93-XX) 260 Calculus of variations and optimal control; optimization (49-XX) 251 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 210 Numerical analysis (65-XX) 139 Operator theory (47-XX) 118 Fluid mechanics (76-XX) 108 Differential geometry (53-XX) 84 Ordinary differential equations (34-XX) 81 Dynamical systems and ergodic theory (37-XX) 77 Functional analysis (46-XX) 71 Global analysis, analysis on manifolds (58-XX) 58 Statistical mechanics, structure of matter (82-XX) 50 Operations research, mathematical programming (90-XX) 40 Integral equations (45-XX) 37 Potential theory (31-XX) 32 Several complex variables and analytic spaces (32-XX) 32 Harmonic analysis on Euclidean spaces (42-XX) 32 Statistics (62-XX) 31 Real functions (26-XX) 31 Biology and other natural sciences (92-XX) 20 Mechanics of deformable solids (74-XX) 16 Mechanics of particles and systems (70-XX) 15 Measure and integration (28-XX) 14 Difference and functional equations (39-XX) 14 Classical thermodynamics, heat transfer (80-XX) 12 Convex and discrete geometry (52-XX) 12 Quantum theory (81-XX) 8 Approximations and expansions (41-XX) 7 Functions of a complex variable (30-XX) 5 Topological groups, Lie groups (22-XX) 5 Abstract harmonic analysis (43-XX) 4 History and biography (01-XX) 4 Algebraic geometry (14-XX) 4 Geophysics (86-XX) 3 Combinatorics (05-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Special functions (33-XX) 3 Optics, electromagnetic theory (78-XX) 2 General and overarching topics; collections (00-XX) 2 Mathematical logic and foundations (03-XX) 2 Integral transforms, operational calculus (44-XX) 2 Computer science (68-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX)

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