N. Krylov

发表

Regularity and global bounds of densities of invariant measures of diffusion processes

V. Bogachev, N. Krylov, M. Röckner, 2005 .

Introduction to the theory of diffusion processes

N. Krylov, 1994 .

Introduction to the Theory of Random Processes

N. Krylov, N. Krylov, 2002 .

On diffusion approximation with discontinuous coefficients

N. Krylov, R. Liptser, 2002, math/0204289.

Statistics and control of stochastic processes

N. Krylov, Alʹbert Nikolaevich Shiri︠a︡ev, R. S. Lipt︠s︡er, 1985 .

ON THE SELECTION OF A MARKOV PROCESS FROM A SYSTEM OF PROCESSES AND THE CONSTRUCTION OF QUASI-DIFFUSION PROCESSES

N. Krylov, 1973 .

On the general notion of fully nonlinear second-order elliptic equations

N. Krylov, 1995 .

Existence of strong solutions for Itô's stochastic equations via approximations

I. Gyöngy, N. Krylov, N. Krylov, 1996 .

Fokker-planck-kolmogorov Equations

Vladimir I. Bogachev, Michael Röckner, S. V. Shaposhnikov, 2015 .

An analytic approach to SPDE’s

N. Krylov, 1999 .

On Kolmogorov’s equations for finite dimensional diffusions

N. Krylov, 1999 .

On the rate of convergence of finite-difference approximations for Bellmans equations with variable coefficients

N. Krylov, 2000 .

On the splitting-up method and stochastic partial differential equations

I. Gyöngy, N. Krylov, 2003 .

On the Rate of Convergence of Splitting-up Approximations for SPDEs

N. Krylov, I. Gyongy, 2003 .

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations

N. Krylov, Nicolai V Krylov, 2018, Mathematical Surveys and Monographs.

A review of some new results in the theory of linear elliptic equations with drift in $$L_{d}$$

N. Krylov, 2021 .

Linear and fully nonlinear elliptic equations with Ld -drift

N. Krylov, 2020, Communications in Partial Differential Equations.

On stochastic It\^o processes with drift in $L_{d}$

N. Krylov, 2020, 2001.03660.

Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces

N. Krylov, Hongjie Dong, 2018, Calculus of Variations and Partial Differential Equations.

Rubio de Francia extrapolation theorem and related topics in the theory of elliptic and parabolic equations. A survey

N. Krylov, 2019, St. Petersburg Mathematical Journal.

Stochastic flows and stochastic differential equations

N. Krylov, 1994 .

Filtering of Finite-State Time-Nonhomogeneous Markov Processes, a Direct Approach

A. Zatezalo, N. Krylov, Nicolai V Krylov, 2000 .

Filtering and Prediction: A Primer

B. Fristedt, N. Krylov, N. Jain, 2007 .

Stochastic partial differential equations and diffusion processes

Boris Rozovskii, B. Rozovskii, N. Krylov, 1982 .

ON THE CAUCHY PROBLEM FOR LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

B. Rozovskii, N. Krylov, Nicolai V Krylov, 1977 .

ON ESTIMATES OF THE MAXIMUM OF A SOLUTION OF A PARABOLIC EQUATION AND ESTIMATES OF THE DISTRIBUTION OF A SEMIMARTINGALE

N. Krylov, 1987 .

On weak uniqueness for some diffusions with discontinuous coefficients

N. Krylov, Nicolai V Krylov, 2004 .

Strong solutions of stochastic equations with singular time dependent drift

Michael Röckner, N. Krylov, M. Röckner, 2005 .

RESTORATION OF WELL-POSEDNESS OF INFINITE-DIMENSIONAL SINGULAR ODE ’ S VIA NOISE

I. Gyöngy, N. Krylov, M. Röckner, 2019 .

Some properties of weighted Sobolev spaces in $\mathbb {R}^d_+$

N. Krylov, 1999 .

SPDEs in $L_q( ( 0,\tau ] , L_p)$ Spaces

N. Krylov, 2000 .

Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms

N. Krylov, 2007 .

Parabolic equations with VMO coefficients in spaces with mixed norms

N. Krylov, 2006, math/0610955.

The Wiener process

N. Krylov, Nicolai V Krylov, 2002 .

A supermartingale characterization of sets of stochastic integrals and applications

N. Krylov, 2002 .

Mean value theorems for stochastic integrals

N. Krylov, 2001 .

An Accelerated Splitting-up Method for Parabolic Equations

I. Gyöngy, N. Krylov, 2004, SIAM J. Math. Anal..

On diffusion approximation with discontinuous coefficients

N. Krylov, R. Liptser, 2002, math/0204289.

9th International Conference on Stochastic Analysis and its Applications

Jonas M. Tölle, Minoru W. Yoshida, J. Norris, 2018 .

Ito formula in banach spaces

I. Gyöngy, N. Krylov, 1981 .

A Simple Proof of a Result of A

N. Krylov, 2001, math/0207013.

A BRIEF OVERVIEW OF THE Lp-THEORY OF SPDES

N. Krylov, 2008 .

Accelerated Numerical Schemes for PDEs and SPDEs

I. Gyöngy, N. Krylov, 2011 .

Expansion of solutions of parameterized equations and acceleration of numerical methods

N. Krylov, I. Gyongy, 2006 .

On averaging principle for diffusion processes with null-recurrent fast component

R. Khasminskii, N. Krylov, 2001 .

Quasiderivatives and Interior Smoothness of Harmonic Functions Associated with Degenerate Diffusion Processes

N. Krylov, 2004 .

Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation

N. Krylov, 1976 .

On stochastic Itô processes with drift in Ld

N. Krylov, 2021 .

About Pogorelov's Method and Aleksandrov's Estimates

N. Krylov, 2020 .

Weighted Parabolic Aleksandrov Estimates: PDE and Stochastic Versions

N. Krylov, 2019, Journal of Mathematical Sciences.

On di!usion approximation with discontinuous coe$cients

N. Krylov, R. Liptser, 2002 .

Traditional proof of Bellman's equation for controlled diffusion processes

N. Krylov, 1981 .

ON THE MAXIMUM PRINCIPLE FOR NONLINEAR PARABOLIC AND ELLIPTIC EQUATIONS

N. Krylov, 1979 .

Some Properties of the Normal Image of Convex Functions

N. Krylov, 1978 .

On time-inhomogeneous controlled diffusion processes in domains

N. Krylov, Hongjie Dong, 2005, math/0512200.

Two Sufficient Conditions for the Regularity of Lateral Boundary for the Heat Equation

N. Krylov, 2002 .

Stochastic evolution equations

B. Rozovskii, N. Krylov, N. V. Krylov, 1981 .

On C1+α regularity of solutions of Isaacs parabolic equations with VMO coefficients

N. Krylov, 2014 .

On fully nonlinear elliptic and parabolic equations in domains with VMO coefficients

N. Krylov, Hongjie Dong, Xu Li, 2010, 1008.3374.

On $C^{1+\alpha}$ regularity of solutions of Isaacs parabolic equations with VMO coefficients

N. Krylov, 2012, 1211.4882.

BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS IN A DOMAIN

N. Krylov, Nicolai V Krylov, 1984 .

Aleksandrov’s estimates for elliptic equations with drift in a Morrey spaces containing 𝐿_{𝑑}

N. Krylov, Hongjie Dong, 2021, 2103.03955.

Elliptic regularity and essential self-adjointness of Dirichlet operators on R

N. Krylov, 1996 .

On Lp-theory of stochastic partial di6erential equations in the whole space

Nicolai V. Krylov, N. Krylov, 1996 .

Elliptic Differential Equations with Coefficients Measurable with Respect to One Variable and VMO with Respect to the Others

Nicolai V. Krylov, Doyoon Kim, N. Krylov, 2007, SIAM J. Math. Anal..

Parabolic equations with VMO coefficients in spaces with mixed norms

N. Krylov, 2006, math/0610955.

A parabolic Littlewood-Paley inequality with applications to parabolic equations

N. Krylov, 1994 .

BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS

N. Krylov, Nicolai V Krylov, 1983 .

A CERTAIN PROPERTY OF SOLUTIONS OF PARABOLIC EQUATIONS WITH MEASURABLE COEFFICIENTS

N. Krylov, M. Safonov, Nicolai V Krylov, 1981 .

Itô’s formula for the Lp-norm of stochastic $${W^{1}_{p}}$$ -valued processes

N. Krylov, Nicolai V Krylov, 2008, 0806.1557.

On Time Inhomogeneous Stochastic Itô Equations with Drift in LD+1

N. Krylov, 2020, Ukrainian Mathematical Journal.

On the solvability of degenerate stochastic partial differential equations in Sobolev spaces

I. Gyöngy, N. Krylov, Máté Gerencsér, 2014, Stochastic Partial Differential Equations: Analysis and Computations.

On the solvability of degenerate stochastic partial differential equations in Sobolev spaces

István Gyöngy, Máté Gerencsér, I. Gyöngy, 2014, 1404.4401.

H\"ormander's theorem for stochastic partial differential equations

N. Krylov, N.V. Krylov, 2013, 1309.5543.

On stochastics equations with respect to semimartingales ii. itô formula in banach spaces

I. Gyöngy, N. Krylov, 1982 .

On stochastic equations with respect to semimartingales I.

István Gyöngy, I. Gyöngy, N. Krylov, 1980 .

Stochastic partial differential equations with unbounded coefficients and applications. III

N. Krylov, I. Gyongy, 1990 .

Characteristics of degenerating second-order parabolic Ito equations

B. Rozovskii, N. Krylov, N. V. Krylov, 1986 .

On SPDE's and superdiffusions

N. Krylov, 1997 .

On Divergence Form SPDEs with VMO Coefficients

Nicolai V. Krylov, N. Krylov, 2008, SIAM J. Math. Anal..

On divergence form SPDEs with VMO coefficients in a half space

N. Krylov, 2008, 0806.1963.

On SPDEs with Variable Coefficients in One Space Dimension

N. Krylov, Kyeong-Hun Kim, 2004 .

A Sobolev space theory of SPDEs with constant coefficients on a half line

S. Lototsky, N. Krylov, 1999 .

Lectures on Elliptic and Parabolic Equations in Holder Spaces

N. Krylov, Nicolai V Krylov, 1996 .

On The Sobolev Space Theory of Parabolic and Elliptic Equations in C1 Domains

Nicolai V. Krylov, Kyeong-Hun Kim, N. Krylov, 2004, SIAM J. Math. Anal..

A Sobolev Space Theory of SPDEs with Constant Coefficients in a Half Space

Nicolai V. Krylov, Sergey V. Lototsky, S. Lototsky, 1999, SIAM J. Math. Anal..

Weighted sobolev spaces and laplace's equation and the heat equations in a half space

N. Krylov, 1999 .

Some Properties of Traces for Stochastic and Deterministic Parabolic Weighted Sobolev Spaces

N. Krylov, 2001 .

The Heat Equation in Lq((0, T), Lp)-Spaces with Weights

Nicolai V. Krylov, N. Krylov, 2001, SIAM J. Math. Anal..

Elliptic equations for measures : Regularity and global bounds of densities

V. Bogachev, N. Krylov, M. Röckner, 2006 .

Regularity of Invariant Measures: The Case of Non-constant Diffusion Part

V. Bogachev, N. Krylov, M. Röckner, 1996 .

Elliptic equations with VMO a, b$\in L_{d}$, and c$\in L_{d/2}$

N. Krylov, 2020, 2004.01778.

On stochastic equations with drift in Ld

N. V. Krylov, N. Krylov, 2020, The Annals of Probability.

ON EQUATIONS OF MINIMAX TYPE IN THE THEORY OF ELLIPTIC AND PARABOLIC EQUATIONS IN THE PLANE

N. Krylov, 1970 .

Rate of convergence of finite-difference approximations for degenerate linear parabolic equations with C1 and C2 coefficients

Nicolai V. Krylov, Hongjie Dong, N. Krylov, 2005 .

On stochastic partial differential equations with Unbounded coefficients

I. Gyöngy, N. Krylov, 1992 .

On the rate of convergence of finite-difference approximations for Bellman equations with constant coefficients

Hongjie Dong, N. Krylov, Hongjie Dong, 2006 .

Accelerated Finite Difference Schemes for Linear Stochastic Partial Differential Equations in the Whole Space

Nicolai V. Krylov, István Gyöngy, I. Gyöngy, 2010, SIAM J. Math. Anal..

PR ] 7 J un 2 01 0 ACCELERATED FINITE DIFFERENCE SCHEMES FOR LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN THE WHOLE

N. Krylov, I. Gyongy, 2010 .

Accelerated finite difference schemes for second order degenerate elliptic and parabolic problems in the whole space

Nicolai V. Krylov, István Gyöngy, I. Gyöngy, 2009, Math. Comput..

Second-order elliptic and parabolic equations with $B(\mathbb R^{2}, VMO)$ coefficients

N. Krylov, Hongjie Dong, 2008 .

ON A CLASS OF NONLINEAR EQUATIONS IN A SPACE OF MEASURABLE FUNCTIONS

N. Krylov, 1969 .

Large deviations for occupation times of Markov processes with L2 semigroups

N. Krylov, N. Jain, Nicolai Krylov, 2007, 0707.4469.

G-convergence of elliptic operators in nondivergence form

N. Krylov, 1985 .

On a Problem Suggested by A.D. Wentzell

N. Krylov, M. Safonov, 1994 .

AW2n-theory of the Dirichlet problem for SPDEs in general smooth domains

N. Krylov, Nicolai V Krylov, 1994 .

A Simple Proof of the Existence of a Solution of Itô’s Equation with Monotone Coefficients

N. V. Krylov, N. Krylov, 1991 .

ON UNIQUENESS OF THE SOLUTION OF BELLMAN'S EQUATION

N. Krylov, 1971 .

Control of a Solution of a Stochastic Integral Equation

N. V. Krylov, N. Krylov, 1972 .

On One-Point Weak Uniqueness for Elliptic Equations

N. Krylov, 1992 .

Second-order eliptic and parabolic equations with B (r2, V MO) coefficients

N. Krylov, Hongjie Dong, 2008, 0810.2739.

ON THE UNIQUENESS OF SUPPORTS OF ANALYTIC FUNCTIONALS

N. Krylov, A. Ramm, Shin-ichi Nakamura, 2017 .

Fully nonlinear second order elliptic equations : recent development

N. Krylov, 1997 .

Nonlinear analysis on Manifolds: Monge-Ampère equations

N. V. Krylov, Anatoliĭ Timofeevich Fomenko, N. Krylov, 1987 .

On Shige Peng’s central limit theorem

N. Krylov, 2018, Stochastic Processes and their Applications.

On the limit passage in parabolic bellman equations

N. Krylov, 1979 .

SOME ESTIMATES OF THE PROBABILITY DENSITY OF A STOCHASTIC INTEGRAL

N. Krylov, 1974 .

On diffusion processes with $$B({\mathbb {R}}^{2}, VMO)$$ coefficients and “good” Green’s functions of the corresponding operators

N. Krylov, 2019, Calculus of Variations and Partial Differential Equations.

Parabolic Equations with Measurable Coefficients

N. Krylov, Doyoon Kim, Nicolai V Krylov, 2006, math/0604124.

ON DEGENERATE NONLINEAR ELLIPTIC EQUATIONS

N. Krylov, 1984 .

Weak interior second order derivative estimates for degenerate nonlinear elliptic equations

N. Krylov, 1994, Differential and Integral Equations.

Weighted sobolev spaces and the heat equation in the whole space

N. Krylov, 1998 .

BOUNDED INHOMOGENEOUS NONLINEAR ELLIPTIC AND PARABOLIC EQUATIONS IN THE PLANE

N. Krylov, 1970 .

Approximating Value Functions for Controlled Degenerate Diffusion Processes by Using Piece-Wise Constant Policies

N. Krylov, Nicolai V Krylov, 1999 .

The Rate of Convergence of Finite-Difference Approximations for Parabolic Bellman Equations with Lipschitz Coefficients in Cylindrical Domains

Hongjie Dong, N. Krylov, Hongjie Dong, 2007 .

The Rate of Convergence of Finite-Difference Approximations for Bellman Equations with Lipschitz Coefficients

N. Krylov, 2004, math/0411248.

Poisson Stochastic Process and Basic Schauder and Sobolev Estimates in the Theory of Parabolic Equations

N. Krylov, E. Priola, 2016, 1607.00957.

On the It\^o-Wentzell formula for distribution-valued processes and related topics

N. Krylov, 2009, 0904.2752.

Hörmander's Theorem for Parabolic Equations with Coefficients Measurable in the Time Variable

Nicolai V. Krylov, N. Krylov, 2013, SIAM J. Math. Anal..

A relatively short proof of Itô’s formula for SPDEs and its applications

N. Krylov, 2012, 1208.3709.

On Bellman's Equations with VMO Coefficients

N. Krylov, 2009, 0912.4987.

Hypoellipticity for filtering problems of partially observable diffusion processes

N. Krylov, 2013, 1309.5545.

On singularity as a function of time of a conditional distribution of an exit time

N. Krylov, 2013, 1306.3934.

Filtering partially observable diffusions up to the exit time from a domain

N. Krylov, Teng Wang, 2011 .

SPDEs in divergence form with VMO coefficients and filtering theory of partially observable diffusion processes with Lipschitz coefficients

N. Krylov, 2009, 0903.0877.

On Parabolic Pdes and Spdes in Sobolev Spaces W P 2 without and with Weights

N. Krylov, 2008 .

One more square root law for Brownian motion and its application to SPDEs

N. Krylov, 2003 .

Nonlinear Elliptic and Parabolic Equations of the Second Order Equations

Nicolai V. Krylov, N. Krylov, 1987 .

On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains

N. Krylov, Hongjie Dong, Xu Li, 2012 .

Smoothness of the value function for a controlled diffusion process in a domain

N. Krylov, 1990 .

On a result of C. Mueller and E. Perkins

N. Krylov, 1997 .

ON CONDITIONAL DISTRIBUTIONS OF DIFFUSION PROCESSES

B. Rozovskii, N. Krylov, 1978 .

On the Itô–Wentzell formula for distribution-valued processes and related topics

N. Krylov, Nicolai V Krylov, 2011 .

Brownian Trajectory Is a Regular Lateral Boundary for the Heat Equation

Nicolai V. Krylov, N. Krylov, 2003, SIAM J. Math. Anal..

PARADOXES OF LIMIT PASSAGE IN SOLUTIONS OF BOUNDARY VALUE PROBLEMS INVOLVING THE APPROXIMATION OF SMOOTH DOMAINS BY POLYGONAL DOMAINS

N. Krylov, G. Sierra, Yu. A. Dubinskii, 2016 .

Introduction to Stochastic Calculus

N. Krylov, 1998 .

On Divergence Form Second-order PDEs with Growing Coefficients in W 1 p Spaces without Weights

N. Krylov, 2009, 0909.5248.

On an energy equality in the theory of evolution equations

N. Krylov, 2016, 1611.09773.

On nonequivalence of regular boundary points for second-order elliptic operators

N. Krylov, N. Krylov, Timur Yastrzhembskiy, 2016, 1606.06346.

On regularity properties and approximations of value functions for stochastic differential games in domains

N. Krylov, 2012, 1207.3758.

A supermartingale characterization of a set of stochastic integrals

N. Krylov, 1989 .

SOME NEW RESULTS IN THE THEORY OF CONTROLLED DIFFUSION PROCESSES

N. Krylov, Nicolai V Krylov, 1980 .

On passing to the limit in degenerate bellman equations. ii

N. Krylov, 1978 .

ON MOMENT ESTIMATES FOR QUASIDERIVATIVES OF SOLUTIONS OF STOCHASTIC EQUATIONS WITH RESPECT TO THE INITIAL DATA, AND THEIR APPLICATION

N. Krylov, 1989 .

ON THE LIMIT DISTRIBUTION OF KOLMOGOROV-SMIRNOV STATISTICS FOR A COMPOSITE HYPOTHESIS

N. Krylov, O. Smolyanov, Boundedly Nonhomogeneous Elliptic, 2016 .

The Calderón-Zygmund Theorem and Parabolic Equations in L P (R, C2+)-Spaces

N. Krylov, 2009 .

On the Foundation of the Lp-Theory of Stochastic Partial Differential Equations

N. Krylov, 2005 .

Stochastic PDE's and Kolmogorov equations in infinite dimensions : lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, August 24- September 1, 1998

Centro internazionale matematico estivo. Session, Centro internazionale matematico estivo, J. Zabczyk, 1999 .

On the estimation of parameters for linear stochastic differential equations

R. Khasminskii, N. Krylov, N. Moshchuk, 1999 .

On Itô’s Stochastic Integral Equations

N. V. Krylov, N. Krylov, 1969 .

Diffusion on a plane with reflection. construction of the process

N. Krylov, 1969 .

Itô stochastic integral

N. Krylov, 2002 .

On parabolic Adams's, the Chiarenza-Frasca theorems, and some other results related to parabolic Morrey spaces

N. Krylov, 2022, Mathematics in Engineering.