Krylov, N. V. (Nikolaĭ Vladimirovich)
Overview
Works:  52 works in 231 publications in 4 languages and 3,340 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other, Contributor 
Classifications:  QA377, 519.233 
Publication Timeline
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Most widely held works by
N. V Krylov
Controlled diffusion processes by
N. V Krylov(
Book
)
33 editions published between 1979 and 2009 in English and held by 415 WorldCat member libraries worldwide
This book deals with the optimal control of solutions of fully observable Ittype stochastic differential equations. The validity of the Bellman differential equation for payoff functions is proved and rules for optimal control strategies are developed. Topics include optimal stopping; one dimensional controlled diffusion; the Lpestimates of stochastic integral distributions; the existence theorem for stochastic equations; the It formula for functions; and the Bellman principle, equation, and normalized equation
33 editions published between 1979 and 2009 in English and held by 415 WorldCat member libraries worldwide
This book deals with the optimal control of solutions of fully observable Ittype stochastic differential equations. The validity of the Bellman differential equation for payoff functions is proved and rules for optimal control strategies are developed. Topics include optimal stopping; one dimensional controlled diffusion; the Lpestimates of stochastic integral distributions; the existence theorem for stochastic equations; the It formula for functions; and the Bellman principle, equation, and normalized equation
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 by
N. V Krylov(
Book
)
22 editions published in 1999 in English and held by 369 WorldCat member libraries worldwide
Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finitedimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LPanalysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results
22 editions published in 1999 in English and held by 369 WorldCat member libraries worldwide
Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finitedimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LPanalysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results
Introduction to the theory of diffusion processes by
N. V Krylov(
Book
)
17 editions published between 1994 and 1999 in English and Italian and held by 359 WorldCat member libraries worldwide
17 editions published between 1994 and 1999 in English and Italian and held by 359 WorldCat member libraries worldwide
Lectures on elliptic and parabolic equations in Hölder spaces by
N. V Krylov(
Book
)
14 editions published between 1900 and 1997 in English and German and held by 277 WorldCat member libraries worldwide
14 editions published between 1900 and 1997 in English and German and held by 277 WorldCat member libraries worldwide
Lectures on elliptic and parabolic equations in Sobolev spaces by
N. V Krylov(
Book
)
14 editions published between 1900 and 2008 in English and held by 260 WorldCat member libraries worldwide
"This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces." "The main areas covered in this book are the first boundaryvalue problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundaryvalue problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing wellknown ideas in a selfcontained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with VMO coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material." "After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequisites are basics of measure theory, the theory of L[subscript p] spaces, and the Fourier transform."Jacket
14 editions published between 1900 and 2008 in English and held by 260 WorldCat member libraries worldwide
"This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces." "The main areas covered in this book are the first boundaryvalue problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundaryvalue problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing wellknown ideas in a selfcontained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with VMO coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material." "After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequisites are basics of measure theory, the theory of L[subscript p] spaces, and the Fourier transform."Jacket
Introduction to the theory of random processes by
N. V Krylov(
Book
)
13 editions published in 2002 in English and held by 257 WorldCat member libraries worldwide
This book concentrates on some general facts and ideas of the theory of stochastic processes. The topics include the Wiener process, stationary processes, infinitely divisible processes, and Ito stochastic equations. Basics of discrete time martingales are also presented and then used in one way or another throughout the book. Another common feature of the main body of the book is using stochastic integration with respect to random orthogonal measures. In particular, it is used for spectral representation of trajectories of stationary processes and for proving that Gaussian stationary processes with rational spectral densities are components of solutions to stochastic equations. In the case of infinitely divisible processes, stochastic integration allows for obtaining a representation of trajectories through jump measures. The Ito stochastic integral is also introduced as a particular case of stochastic integrals with respect to random orthogonal measures. Although it is not possible to cover even a noticeable portion of the topics listed above in a short book, it is hoped that after having followed the material presented here, the reader will have acquired a good understanding of what kind of results are available and what kind of techniques are used to obtain them. With more than 100 problems included, the book can serve as a text for an introductory course on stochastic processes or for independent study. Other works by this author published by the AMS include, Lectures on Elliptic and Parabolic Equations in Holder Spaces and Introduction to the Theory of Diffusion Processes
13 editions published in 2002 in English and held by 257 WorldCat member libraries worldwide
This book concentrates on some general facts and ideas of the theory of stochastic processes. The topics include the Wiener process, stationary processes, infinitely divisible processes, and Ito stochastic equations. Basics of discrete time martingales are also presented and then used in one way or another throughout the book. Another common feature of the main body of the book is using stochastic integration with respect to random orthogonal measures. In particular, it is used for spectral representation of trajectories of stationary processes and for proving that Gaussian stationary processes with rational spectral densities are components of solutions to stochastic equations. In the case of infinitely divisible processes, stochastic integration allows for obtaining a representation of trajectories through jump measures. The Ito stochastic integral is also introduced as a particular case of stochastic integrals with respect to random orthogonal measures. Although it is not possible to cover even a noticeable portion of the topics listed above in a short book, it is hoped that after having followed the material presented here, the reader will have acquired a good understanding of what kind of results are available and what kind of techniques are used to obtain them. With more than 100 problems included, the book can serve as a text for an introductory course on stochastic processes or for independent study. Other works by this author published by the AMS include, Lectures on Elliptic and Parabolic Equations in Holder Spaces and Introduction to the Theory of Diffusion Processes
Nonlinear elliptic and parabolic equations of the second order by
N. V Krylov(
Book
)
13 editions published between 1985 and 2001 in English and held by 253 WorldCat member libraries worldwide
13 editions published between 1985 and 2001 in English and held by 253 WorldCat member libraries worldwide
Filtering and prediction : a primer by
Bert Fristedt(
Book
)
12 editions published between 2007 and 2008 in English and held by 237 WorldCat member libraries worldwide
12 editions published between 2007 and 2008 in English and held by 237 WorldCat member libraries worldwide
Statistics and control of stochastic processes by
Steklov Seminar(
Book
)
10 editions published between 1984 and 1985 in 3 languages and held by 204 WorldCat member libraries worldwide
10 editions published between 1984 and 1985 in 3 languages and held by 204 WorldCat member libraries worldwide
FokkerPlanckKolmogorov equations by
V. I Bogachev(
Book
)
9 editions published in 2015 in English and held by 165 WorldCat member libraries worldwide
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are FokkerPlanckKolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations
9 editions published in 2015 in English and held by 165 WorldCat member libraries worldwide
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are FokkerPlanckKolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations
Upravli︠a︡emye prot︠s︡essy diffuzionnogo tipa by
N. V Krylov(
Book
)
5 editions published in 1977 in Russian and held by 26 WorldCat member libraries worldwide
5 editions published in 1977 in Russian and held by 26 WorldCat member libraries worldwide
Nelineĭnye ėllipticheskie i parabolicheskie uravnenii︠a︡ vtorogo pori︠a︡dka by
N. V Krylov(
Book
)
4 editions published in 1985 in Russian and held by 26 WorldCat member libraries worldwide
4 editions published in 1985 in Russian and held by 26 WorldCat member libraries worldwide
Probabilistic methods of investigating interior smoothness of harmonic functions associated with degenerate elliptic operators by
N. V Krylov(
Book
)
3 editions published in 2004 in English and held by 19 WorldCat member libraries worldwide
3 editions published in 2004 in English and held by 19 WorldCat member libraries worldwide
Upravljaemye processy diffuzionnogo tipa by
N. V Krylov(
Book
)
2 editions published in 1977 in Russian and held by 10 WorldCat member libraries worldwide
2 editions published in 1977 in Russian and held by 10 WorldCat member libraries worldwide
On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions by
V. I Bogachev(
Book
)
2 editions published in 1999 in English and held by 9 WorldCat member libraries worldwide
2 editions published in 1999 in English and held by 9 WorldCat member libraries worldwide
Nelinejnye ėlliptičeskie i paraboličeskie uravnenija vtorogo porjadka by
N. V Krylov(
Book
)
2 editions published in 1985 in Undetermined and held by 9 WorldCat member libraries worldwide
2 editions published in 1985 in Undetermined and held by 9 WorldCat member libraries worldwide
Elliptiv regularity and essential selfadjointness of Dirichlet operators on Rn by
V. I Bogachev(
Book
)
3 editions published in 1996 in English and held by 8 WorldCat member libraries worldwide
3 editions published in 1996 in English and held by 8 WorldCat member libraries worldwide
Introduction to nonlinear mechanics by
N. M Krylov(
Book
)
3 editions published between 1947 and 1970 in English and held by 8 WorldCat member libraries worldwide
The book description for the forthcoming "Introduction to NonLinear Mechanics. (AM11)" is not yet available
3 editions published between 1947 and 1970 in English and held by 8 WorldCat member libraries worldwide
The book description for the forthcoming "Introduction to NonLinear Mechanics. (AM11)" is not yet available
Some properties of traces for stochastic and deterministic parabolic weighted Soboloev spaces by
N. V Krylov(
Book
)
2 editions published in 1999 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 1999 in English and held by 8 WorldCat member libraries worldwide
Regularity of invariant measures : the case of nonconstant diffusion part by
V. I Bogachev(
Book
)
4 editions published in 1995 in English and German and held by 8 WorldCat member libraries worldwide
4 editions published in 1995 in English and German and held by 8 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Röckner, Michael 1956 Other
 Zabczyk, Jerzy Other
 Da Prato, Giuseppe Other Editor
 Centro internazionale matematico estivo
 Balakrishnan, A. V.
 Jain, N. (Naresh) 1937
 Fristedt, Bert 1937 Author
 Bogachev, V. I. (Vladimir Igorevich) 1961 Author
 Shiri︠a︡ev, Alʹbert Nikolaevich
 Novikov, A. A. mathematician Editor
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Associated Subjects
Control theory Differential equations Differential equations, Elliptic Differential equations, Hyperbolic Differential equations, Nonlinear Differential equations, NonlinearNumerical solutions Differential equations, Parabolic Differential equations, Partial Diffusion processes Distribution (Probability theory) Elliptic operators Equations Filters (Mathematics) FokkerPlanck equation Gaussian processes Generalized spaces Harmonic functions Markov processes Mathematical statistics Mathematics Mechanics, Analytic Nonlinear mechanics Oscillations Prediction theory Sobolev spaces Stochastic analysis Stochastic control theory Stochastic differential equations Stochastic partial differential equations Stochastic processes
Alternative Names
Krilov , Nicolai V.
Krilov , Nikolãi Vladimirovič
Kryloff , N.
Krylov, N.
Krylov, N.V.
Krylov, N.V. 1941
Krylov, Nicolai 1941
Krylov, Nicolai V.
Krylov, Nicolai V. 1941
Krylov, Nikolai
Krylov, Nikolai 1941
Krylov, Nikolai A. 1941
Krylov, Nikolai V. 1941
Krylov, Nikolaĭ Vladimirovich.
Krylov, Nikolaĭ Vladimirovich 1941
Krylov , Nikolaj Vladimirovic
Krylov, Nikolaj Vladimirovič 1941
Krylov , Nikolaj Vladimirovich
Krylow , N. W.
Nicolai Krylov
Nicolai V. Krylov matemático ruso
Nicolai V. Krylov Russian mathematician
Nikolai Wladimirowitsch Krylow mathématicien russe
Nikolai Wladimirowitsch Krylow Russisch wiskundige
Nikolai Wladimirowitsch Krylow russischer Mathematiker
Крылов, Николай Владимирович.
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