WorldCat Identities

Krylov, N. V. (Nikolaĭ Vladimirovich)

Overview
Works: 46 works in 205 publications in 4 languages and 3,174 library holdings
Genres: Conference papers and proceedings 
Roles: Author, Editor, Contributor, Other
Classifications: QA274, 519.23
Publication Timeline
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Most widely held works by N. V Krylov
Controlled diffusion processes by N. V Krylov( Book )

32 editions published between 1977 and 2009 in English and Russian and held by 430 WorldCat member libraries worldwide

This book deals with the optimal control of solutions of fully observable It-type 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 Lp-estimates 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 360 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 finite-dimensional equations, giving existence, uniqueness and regularity results. M. Rckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis 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 )

15 editions published between 1994 and 1999 in English and Russian and held by 354 WorldCat member libraries worldwide

Nonlinear elliptic and parabolic equations of the second order by N. V Krylov( Book )

17 editions published between 1985 and 1992 in 3 languages and held by 277 WorldCat member libraries worldwide

Lectures on elliptic and parabolic equations in Hölder spaces by N. V Krylov( Book )

13 editions published between 1900 and 1997 in English and held by 267 WorldCat member libraries worldwide

Introduction to the theory of random processes by N. V Krylov( Book )

13 editions published in 2002 in English and held by 255 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
Lectures on elliptic and parabolic equations in Sobolev spaces by N. V Krylov( Book )

12 editions published between 1900 and 2008 in English and held by 253 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 boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundary-value problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing well-known ideas in a self-contained 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
Filtering and prediction : a primer by Bert Fristedt( Book )

12 editions published between 2007 and 2008 in English and held by 234 WorldCat member libraries worldwide

Statistics of random processes by R. Sh Lipt︠s︡er( Book )

10 editions published between 1984 and 1985 in 3 languages and held by 205 WorldCat member libraries worldwide

The subject of these two volumes is non-linear filtering (prediction and smoothing) theory and its application to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. The required mathematical background is presented in the first volume: the theory of martingales, stochastic differential equations, the absolute continuity of probability measures for diffusion and Ito processes, elements of stochastic calculus for counting processes. The book is not only addressed to mathematicians but should also serve the interests of other scientists who apply probabilistic and statistical methods in their work. The theory of martingales presented in the book has an independent interest in connection with problems from financial mathematics. In the second edition, the authors have made numerous corrections, updating every chapter, adding two new subsections devoted to the Kalman filter under wrong initial conditions, as well as a new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years
Fokker-Planck-Kolmogorov equations by V. I Bogachev( Book )

5 editions published in 2015 in English and held by 145 WorldCat member libraries worldwide

Géométrie descriptive by N. V Krylov( Book )

1 edition published in 1971 in French and held by 20 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 17 WorldCat member libraries worldwide

Elliptiv regularity and essential self-adjointness of Dirichlet operators on Rn by V. I Bogachev( Book )

4 editions published in 1996 in English and held by 9 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

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

Introduction to non-linear mechanics by N. M Krylov( Book )

3 editions published between 1947 and 1970 in English and held by 6 WorldCat member libraries worldwide

Lectures on fully nonlinear second order elliptic equations by N. V Krylov( Book )

3 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide

Lekt︠s︡ii po ėlliptickeskim i parabolicheskim uravnenii︠a︡m v prostranstvakh G̈ëlʹdera by N. V Krylov( Book )

3 editions published in 1998 in Russian and held by 4 WorldCat member libraries worldwide

Kratkij spravočnik po sel'skochozjajstvennomu stroitel'stvu by N. V Krylov( Book )

3 editions published in 1958 in Russian and held by 4 WorldCat member libraries worldwide

Lectures on elliptic and parabolic equations in Sobolev spaces by N. V Krylov( )

1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide

 
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Audience level: 0.71 (from 0.60 for Introducti ... to 0.95 for Elliptiv r ...)

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
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 Russian mathematician

Nikolai Wladimirowitsch Krylow mathématicien russe

Nikolai Wladimirowitsch Krylow russischer Mathematiker

Крылов, Николай Владимирович.

Languages
English (152)

Russian (20)

German (1)

French (1)

Covers
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, 1998Nonlinear elliptic and parabolic equations of the second orderIntroduction to the theory of random processesLectures on elliptic and parabolic equations in Sobolev spacesFiltering and prediction : a primerProbabilistic methods of investigating interior smoothness of harmonic functions associated with degenerate elliptic operators