Compute Distance To:
 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: 324 Publications since 1964, including 17 Books 2 Contributions as Editor Biographic References: 1 Publication Co-Authors: 36 Co-Authors with 98 Joint Publications 1,093 Co-Co-Authors
all top 5

Co-Authors

 226 single-authored 22 Gyöngy, István 13 Rozovskii, Boris L. 10 Röckner, Michael 9 Dong, Hongjie 8 Bogachev, Vladimir Igorevich 6 Safonov, Mikhail V. 4 Liptser, Robert 4 Veretennikov, Alexander Yu. 3 Genis, I. L. 3 Khas’minskiĭ, Rafail Zalmanovich 3 Priola, Enrico 3 Shiryaev, Al’bert Nikolaevich 3 Yushkevich, Aleksandr Adol’fovich 2 Anulova, Svetlana 2 Jain, Naresh C. 2 Kim, Doyoon 2 Kim, KyeongHun 2 Lototsky, Sergey V. 2 Miroshnichenko, T. P. 2 Nosovskij, G. V. 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 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 11 Stochastic Processes and their Applications 10 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 9 Applied Mathematics and Optimization 8 Teoriya Veroyatnosteĭ i eë Primeneniya 8 The Annals of Probability 8 St. Petersburg Mathematical Journal 7 Soviet Mathematics. Doklady 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 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 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 Collectanea Mathematica 1 Proceedings of the American Mathematical Society 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 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 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
all top 5

Fields

 176 Probability theory and stochastic processes (60-XX) 175 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) 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 History and biography (01-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

262 Publications have been cited 4,631 times in 2,804 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
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 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
Lectures on elliptic and parabolic equations in Sobolev spaces. Zbl 1147.35001
Krylov, N. V.
2008
Parabolic and elliptic equations with VMO coefficients. Zbl 1114.35079
Krylov, N. V.
2007
An analytic approach to SPDEs. Zbl 0933.60073
Krylov, N. V.
1999
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
Fokker-Planck-Kolmogorov equations. Zbl 1342.35002
Bogachev, Vladimir I.; Krylov, Nicolai V.; Röckner, Michael; Shaposhnikov, Stanislav V.
2015
Nonlinear elliptic and parabolic equations of second order. (Нелинейные ѐллиптические и параболические уравнения второго порядка.) Zbl 0586.35002
Krylov, N. V.
1985
Controlled processes of diffusion type. (Управляемые процессы диффузионного типа.) Zbl 0513.60043
Krylov, N. V.
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.
2007
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
Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms. Zbl 1133.35052
Krylov, N. V.
2007
On the rate of convergence of finite-difference approximations for Bellman’s equations with variable coefficients. Zbl 0971.65081
Krylov, N. V.
2000
Introduction to the theory of diffusion processes. Transl. from the Russian by V. Khidekel a. G. Pasechnik. Zbl 0844.60050
Krylov, N. V.
1995
Elliptic and parabolic equations for measures. Zbl 1194.35481
Bogachev, V. I.; Krylov, N. V.; Röckner, M.
2009
On $$L_ p$$-theory of stochastic partial differential equations in the whole space. Zbl 0846.60061
Krylov, N. V.
1996
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
Second-order elliptic equations with variably partially VMO coefficients. Zbl 1171.35352
Krylov, N. V.
2009
On stochastic equations with respect to semimartingales I. Zbl 0439.60061
Gyöngy, I.; Krylov, N. V.
1980
Parabolic equations with measurable coefficients. Zbl 1124.35024
Kim, Doyoon; Krylov, N. V.
2007
A $$W_ 2^ n$$-theory of the Dirichlet problem for SPDEs in general smooth domains. Zbl 0794.60062
Krylov, N. V.
1994
A Sobolev space theory of SPDEs with constant coefficients in a half space. Zbl 0943.60047
Krylov, N. V.; Lototsky, S. V.
1999
Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation. Zbl 0362.35038
Krylov, N. V.
1976
On the general notion of fully nonlinear second-order elliptic equations. Zbl 0832.35042
Krylov, N. V.
1995
Boundedly nonhomogeneous elliptic and parabolic equations. Zbl 0529.35026
Krylov, N. V.
1983
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 splitting-up method and stochastic partial differential equations. Zbl 1028.60058
Gyöngy, István; Krylov, Nicolai
2003
Boundedly nonhomogeneous elliptic and parabolic equations in a domain. Zbl 0578.35024
Krylov, N. V.
1984
Weighted Sobolev spaces and Laplace’s equation and the heat equations in a half space. Zbl 0934.35032
Krylov, N. V.
1999
On the Sobolev space theory of parabolic and elliptic equations in $$C^{1}$$ domains. Zbl 1083.35041
Kim, Kyeong-Hun; Krylov, N. V.
2004
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
Elliptic and parabolic second-order PDEs with growing coefficients. Zbl 1195.35160
Krylov, N. V.; Priola, E.
2010
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
The heat equation in $$L_{q}((0,T),L_{p})$$-spaces with weights. Zbl 0979.35060
Krylov, N. V.
2001
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
On weak uniqueness for some diffusions with discontinuous coefficients. Zbl 1073.60064
Krylov, N. V.
2004
Itô’s formula for the $$L _{p }$$-norm of stochastic $${W^{1}_{p}}$$-valued processes. Zbl 1232.60050
Krylov, N. V.
2010
Control of a solution of a stochastic integral equation. Zbl 0265.60055
Krylov, N. V.
1972
A Sobolev space theory of SPDE with constant coefficients on a half line. Zbl 0928.60042
Krylov, N. V.; Lototsky, S. V.
1999
Stochastic evolution equations. Zbl 1130.60069
Krylov, Nicolai V.; Rozovskii, Boris L.
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
1997
On the rate of convergence of splitting-up approximations for SPDEs. Zbl 1038.60057
Gyöngy, István; Krylov, Nicolai
2003
A generalization of the Littlewood-Paley inequality and some other results related to stochastic partial differential equations. Zbl 0870.42005
Krylov, N. V.
1994
A relatively short proof of Itô’s formula for SPDEs and its applications. Zbl 1274.60204
Krylov, N. V.
2013
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
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
On Kolmogorov’s equations for finite dimensional diffusions. Zbl 0943.60070
Krylov, N. V.
1999
Regularity of invariant measures: The case of non-constant diffusion part. Zbl 0929.60039
Bogachev, V. I.; Krylov, N.; Röckner, M.
1996
An inequality in the theory of stochastic integrals. Zbl 0238.60038
Krylov, N. V.
1971
On the existence of $$W^2_p$$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions. Zbl 1277.35172
Krylov, N. V.
2013
Stochastic partial differential equations and diffusion processes. Zbl 0518.60072
Krylov, N. V.; Rozovskij, B. L.
1982
On degenerate nonlinear elliptic equations. Zbl 0525.35038
Krylov, N. V.
1983
Accelerated finite difference schemes for linear stochastic partial differential equations in the whole space. Zbl 1222.65009
Gyöngy, István; Krylov, Nicolai
2010
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 conditional distributions of diffusion processes. Zbl 0402.60077
Krylov, N. V.; Rozovskii, B. L.
1978
Second-order elliptic and parabolic equations with $$B(\mathbb R^2, \mathrm{VMO})$$ coefficients. Zbl 1207.35174
Dong, Hongjie; Krylov, N. V.
2010
Introduction to the theory of random processes. Zbl 1008.60001
Krylov, N. V.
2002
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
On characteristics of the degenerate second order Ito parabolic equations. Zbl 0503.60066
Krylov, N. V.; Rozovskij, B. L.
1982
Sobolev and viscosity solutions for fully nonlinear elliptic and parabolic equations. Zbl 1401.35001
Krylov, N. V.
2018
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
Characteristics of degenerate second-order parabolic Ito equations. Zbl 0584.60068
Krylov, N. V.; Rozovskij, B. L.
1986
Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces. Zbl 1418.35211
Dong, Hongjie; Krylov, N. V.
2019
Some properties of weighted Sobolev spaces in $$\mathbb{R}_+^d$$. Zbl 0962.46016
Krylov, Nicolai V.
1999
Smoothness of the value function for a controlled diffusion process in a domain. Zbl 0701.93054
Krylov, N. V.
1990
On SPDEs with variable coefficients in one space dimension. Zbl 1059.60075
Kim, Kyeong-Hun; Krylov, N. V.
2004
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
On the first integrals and Liouville equations for diffusion processes. Zbl 0474.60049
Krylov, N. V.; Rozovskii, B. L.
1981
Stochastic partial differential equations and diffusion processes. Zbl 0508.60054
Krylov, N. V.; Rozovskij, B. L.
1982
On one-point weak uniqueness for elliptic equations. Zbl 0798.35039
Krylov, N. V.
1992
On the rate of convergence of finite-difference approximations for elliptic Isaacs equations in smooth domains. Zbl 1331.65122
Krylov, N. V.
2015
On factorizations of smooth nonnegative matrix-values functions and on smooth functions with values in polyhedra. Zbl 1183.15011
Krylov, N. V.
2008
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
On strong solutions of stochastic differential equations. Zbl 0481.60062
Zvonkin, A. K.; Krylov, N. V.
1975
On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains. Zbl 1278.35133
Dong, Hongjie; Krylov, N. V.; Li, Xu
2013
Control of Markov processes and W-spaces. Zbl 0274.93049
Krylov, N. V.
1972
Explicit formulae for the solutions of stochastic equations. Zbl 0353.60059
Veretennikov, A. Yu.; Krylov, N. V.
1976
On the solvability of degenerate stochastic partial differential equations in Sobolev spaces. Zbl 1310.60094
Gerencsér, Máté; Gyöngy, István; Krylov, Nicolai
2015
SPDEs in $$L_q(\mskip-2mu(0,\tau], L_p)$$ spaces. Zbl 0963.60053
Krylov, N. V.
2000
On the rate of convergence of finite-difference approximations for Bellman’s equations. Zbl 0902.65035
Krylov, N. V.
1997
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 controlled diffusion processes with unbounded coefficients. Zbl 0497.93060
Krylov, N. V.
1981
On the existence of smooth solutions for fully nonlinear elliptic equations with measurable “coefficients” without convexity assumptions. Zbl 1285.35033
Krylov, Nicolai V.
2012
On explicit formulas for solutions of stochastic equations. Zbl 0376.60067
Veretennikov, A. Yu.; Krylov, N. V.
1978
On diffusion processes with drift in $$L_d$$. Zbl 1480.60239
Krylov, N. V.
2021
Elliptic equations with VMO $$a,b\in L_d$$, and $$c\in L_{d/2}$$. Zbl 1460.35069
Krylov, N. V.
2021
On stochastic equations with drift in $${L_d}$$. Zbl 07441180
Krylov, N. V.
2021
On time inhomogeneous stochastic Itô equations with drift in $$L_{D+1}$$. Zbl 1483.60083
Krylov, N. V.
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.
2021
On stochastic Itô processes with drift in $$L_d$$. Zbl 1469.60186
Krylov, N. V.
2021
On strong solutions of Itô’s equations with $$\sigma\in W_{\mathtt{d}}^1$$ and $$\mathtt{b}\in{L_{\mathtt{d}}}$$. Zbl 07467492
Krylov, N. V.
2021
Linear and fully nonlinear elliptic equations with $$L_d$$-drift. Zbl 1460.35141
Krylov, Nicolai V.
2020
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
All functions are locally s-harmonic up to a small error. Zbl 1447.35358
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
Uniqueness for $$L_{p}$$-viscosity solutions for uniformly parabolic Isaacs equations with measurable lower order terms. Zbl 1394.35231
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 $$C^{1+\alpha}$$ regularity of solutions of Isaacs parabolic equations with VMO coefficients. Zbl 1304.35173
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
Hörmander’s theorem for parabolic equations with coefficients measurable in the time variable. Zbl 1288.35315
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
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 fully nonlinear elliptic and parabolic equations with VMO coefficients in domains. Zbl 1278.35133
Dong, Hongjie; Krylov, N. V.; Li, Xu
2013
On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains. Zbl 1287.49027
Krylov, N. V.
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.
2013
An ersatz existence theorem for fully nonlinear parabolic equations without convexity assumptions. Zbl 1295.35262
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 equations for partially observable diffusion processes with Lipschitz continuous coefficients. Zbl 1223.93112
Krylov, N. V.
2011
Filtering partially observable diffusions up to the exit time from a domain. Zbl 1233.62168
Krylov, N. V.; Wang, Teng
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
On parabolic PDEs and SPDEs in Sobolev spaces $$W^2_p$$ without and with weights. Zbl 1152.60046
Krylov, Nicolai V.
2008
A brief overview of the $$L_p$$-theory of SPDEs. Zbl 1224.60161
Krylov, Nicolai
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
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
An accelerated splitting-up method for parabolic equations. Zbl 1101.35038
Gyöngy, István; Krylov, Nicolai
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
...and 162 more Documents
all top 5

Cited by 2,484 Authors

 96 Krylov, Nicolaĭ Vladimirovich 65 Röckner, Michael 53 Shaposhnikov, Stanislav V. 51 Dong, Hongjie 49 Bogachev, Vladimir Igorevich 40 Gyöngy, István 39 Kim, KyeongHun 33 Flandoli, Franco 27 Zheng, Shenzhou 26 Lions, Pierre-Louis 26 Zhang, Xicheng 25 Pragarauskas, Henrikas 23 Kim, Doyoon 22 Mikulevicius, Remigijus 20 Byun, Sun-Sig 19 Kim, Ildoo 18 Da Prato, Giuseppe 17 Trudinger, Neil Sidney 17 Veretennikov, Alexander Yu. 16 Barbu, Viorel 16 Jentzen, Arnulf 16 Wang, Feng-Yu 15 Dareiotis, Konstantinos Anastasios 15 Priola, Enrico 15 Wang, Xu-Jia 14 Ivochkina, Nina Mikhaĭlovna 14 Lorenzi, Luca 14 Luo, Dejun 14 Phan, Tuoc Van 13 Arapostathis, Aristotle 13 Bahlali, Khaled 13 Jakobsen, Espen Robstad 13 Pardoux, Etienne 13 Reisinger, Christoph 13 Veraar, Mark C. 13 Wang, Lihe 13 Wei, Jinlong 13 Yi, Yingfei 12 Lee, Kijung 11 Borkar, Vivek Shripad 11 Brzeźniak, Zdzisław 11 Deugoue, Gabriel 11 Du, Kai 11 Gess, Benjamin 11 Karlsen, Kenneth Hvistendahl 11 Kim, Seick 11 Nualart, David 10 Biswas, Anup 10 Delarue, François 10 Freidlin, Mark I. 10 Gerencsér, Máté 10 Hofmanová, Martina 10 Lieberman, Gary M. 10 Mishura, Yuliya Stepanivna 10 Pham, Huyên 10 Proske, Frank Norbert 10 Rozovskii, Boris L. 10 Zhang, Junjie 10 Zhang, Tusheng S. 9 Caffarelli, Luis Ángel 9 Dokuchaev, Nikolai G. 9 Huang, Xing 9 Ji, Min 9 Karatzas, Ioannis 9 Matoussi, Anis 9 Nazarov, Alexander I. 9 Qiu, Jinniao 9 Razafimandimby, Paul André 9 Safonov, Mikhail V. 9 Sango, Mamadou 9 Sirakov, Boyan Slavchev 9 Świȩch, Andrzej 9 Temam, Roger Meyer 9 Xie, Longjie 8 Arkhipova, Arina A. Arkhipova 8 Bensoussan, Alain 8 Breit, Dominic 8 Cerrai, Sandra 8 Feehan, Paul M. N. 8 Gao, Hongjun 8 Goreac, Dan 8 Grothaus, Martin 8 Hutzenthaler, Martin 8 Kulinich, Grygoriĭ L. 8 Lee, Mikyoung 8 Ouknine, Youssef 8 Pop, Camelia Alexandra 8 Russo, Francesco 8 Ryu, Seungjin 8 Šiška, David 8 Tang, Shanjian 8 Yao, Fengping 7 Bao, Jiguang 7 Bayraktar, Erhan 7 Bramanti, Marco 7 da Silva, João Vítor 7 Feireisl, Eduard 7 Hu, Mingshang 7 Kloeden, Peter Eris 7 Levakov, Anatoliĭ Afanas’evich ...and 2,384 more Authors
all top 5

Cited in 364 Serials

 150 Journal of Differential Equations 145 Stochastic Processes and their Applications 113 Journal of Mathematical Analysis and Applications 91 Journal of Functional Analysis 58 The Annals of Probability 55 Potential Analysis 54 Communications in Partial Differential Equations 51 Probability Theory and Related Fields 51 Calculus of Variations and Partial Differential Equations 49 Journal of Mathematical Sciences (New York) 49 Stochastic and Partial Differential Equations. Analysis and Computations 48 Applied Mathematics and Optimization 47 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 47 Transactions of the American Mathematical Society 46 Stochastic Analysis and Applications 41 SIAM Journal on Control and Optimization 38 The Annals of Applied Probability 37 Archive for Rational Mechanics and Analysis 35 Doklady Mathematics 33 Stochastics and Dynamics 32 Journal of Evolution Equations 31 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 31 Journal de Mathématiques Pures et Appliquées. Neuvième Série 28 Discrete and Continuous Dynamical Systems 27 Advances in Mathematics 25 SIAM Journal on Mathematical Analysis 25 NoDEA. Nonlinear Differential Equations and Applications 24 Journal of Theoretical Probability 24 Communications on Pure and Applied Analysis 23 Lithuanian Mathematical Journal 23 Stochastics 23 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 19 Proceedings of the American Mathematical Society 18 Systems & Control Letters 18 Stochastics 17 Mathematische Annalen 17 The Journal of Geometric Analysis 16 Mathematics of Computation 16 Acta Applicandae Mathematicae 16 Differential Equations 16 Discrete and Continuous Dynamical Systems. Series B 15 Mathematical Notes 15 Journal of Computational and Applied Mathematics 15 Mathematical Finance 14 Mathematische Zeitschrift 14 Statistics & Probability Letters 14 Infinite Dimensional Analysis, Quantum Probability and Related Topics 14 Science China. Mathematics 13 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 13 Siberian Mathematical Journal 13 Bernoulli 13 Finance and Stochastics 13 Acta Mathematica Sinica. English Series 12 Communications in Mathematical Physics 12 Journal für die Reine und Angewandte Mathematik 12 SIAM Journal on Numerical Analysis 12 Bulletin des Sciences Mathématiques 11 Journal of Soviet Mathematics 11 Journal of Economic Dynamics & Control 11 Journal of Dynamics and Differential Equations 11 Comptes Rendus. Mathématique. Académie des Sciences, Paris 11 Nonlinear Analysis. Theory, Methods & Applications 10 Ukrainian Mathematical Journal 10 Duke Mathematical Journal 10 Stochastics and Stochastics Reports 10 Journal of Nonlinear Science 10 St. Petersburg Mathematical Journal 10 Electronic Journal of Probability 10 Nonlinear Analysis. Real World Applications 9 Computers & Mathematics with Applications 9 Communications on Pure and Applied Mathematics 9 Annali di Matematica Pura ed Applicata. Serie Quarta 9 Manuscripta Mathematica 9 Chinese Annals of Mathematics. Series B 8 Nonlinearity 8 Applied Mathematics and Computation 8 Numerische Mathematik 8 European Journal of Operational Research 8 Theory of Probability and Mathematical Statistics 8 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 Communications in Contemporary Mathematics 8 Boundary Value Problems 8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 SIAM Journal on Financial Mathematics 7 International Journal of Control 7 Annales de l’Institut Fourier 7 Automatica 7 Inventiones Mathematicae 7 Journal of Optimization Theory and Applications 7 Journal of Scientific Computing 7 Bulletin of the American Mathematical Society. New Series 7 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 6 Journal of Mathematical Physics 6 Journal of Statistical Physics 6 Theory of Probability and its Applications 6 Acta Mathematica 6 Journal of Applied Probability 6 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 6 Acta Mathematicae Applicatae Sinica. English Series 6 Abstract and Applied Analysis ...and 264 more Serials
all top 5

Cited in 49 Fields

 1,585 Partial differential equations (35-XX) 1,488 Probability theory and stochastic processes (60-XX) 348 Systems theory; control (93-XX) 276 Calculus of variations and optimal control; optimization (49-XX) 270 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 242 Numerical analysis (65-XX) 149 Operator theory (47-XX) 141 Fluid mechanics (76-XX) 124 Differential geometry (53-XX) 94 Ordinary differential equations (34-XX) 89 Functional analysis (46-XX) 88 Dynamical systems and ergodic theory (37-XX) 73 Global analysis, analysis on manifolds (58-XX) 69 Statistical mechanics, structure of matter (82-XX) 56 Operations research, mathematical programming (90-XX) 44 Integral equations (45-XX) 40 Biology and other natural sciences (92-XX) 39 Potential theory (31-XX) 39 Several complex variables and analytic spaces (32-XX) 38 Harmonic analysis on Euclidean spaces (42-XX) 36 Statistics (62-XX) 33 Real functions (26-XX) 20 Mechanics of deformable solids (74-XX) 19 Measure and integration (28-XX) 19 Mechanics of particles and systems (70-XX) 16 Classical thermodynamics, heat transfer (80-XX) 15 Convex and discrete geometry (52-XX) 14 Difference and functional equations (39-XX) 12 Geophysics (86-XX) 11 Quantum theory (81-XX) 7 Functions of a complex variable (30-XX) 7 Approximations and expansions (41-XX) 6 Algebraic geometry (14-XX) 6 Topological groups, Lie groups (22-XX) 5 History and biography (01-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Abstract harmonic analysis (43-XX) 5 Computer science (68-XX) 4 Integral transforms, operational calculus (44-XX) 3 Combinatorics (05-XX) 3 Special functions (33-XX) 3 Optics, electromagnetic theory (78-XX) 2 Mathematical logic and foundations (03-XX) 2 General topology (54-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX)

Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.