Skorokhod, A. V. (Anatoliĭ Vladimirovich) 19302011
Overview
Works:  196 works in 666 publications in 7 languages and 7,596 library holdings 

Roles:  Author, Editor, Adapter 
Classifications:  QA274, 519.2 
Publication Timeline
.
Most widely held works by
A. V Skorokhod
The theory of stochastic processes by
I. I Gikhman(
Book
)
87 editions published between 1971 and 2004 in 4 languages and held by 862 WorldCat member libraries worldwide
From the Reviews: "Gihman and Skorohod have done an excellent job of presenting the theory in its present state of rich imperfection." D.W. Stroock in Bulletin of the American Mathematical Society, 1980 "To call this work encyclopedic would not give an accurate picture of its content and style. Some parts read like a textbook, but others are more technical and contain relatively new results. ... The exposition is robust and explicit, as one has come to expect of the Russian tradition of mathematical writing. The set when completed will be an invaluable source of information and reference in this everexpanding field" K.L. Chung in American Scientist, 1977 "..., the subject has grown enormously since 1953, and there will never be a true successor to Doob's book, but Gihman and Skorohod's three volumes will, I think, occupy a rather similar position as an invaluable tool of reference for all probability theorists. ... The dominant impression is of the authors' mastery of their material, and of their confident insight into its underlying structure. ..." J.F.C. Kingman in Bulletin of the London Mathematical Society, 1977
87 editions published between 1971 and 2004 in 4 languages and held by 862 WorldCat member libraries worldwide
From the Reviews: "Gihman and Skorohod have done an excellent job of presenting the theory in its present state of rich imperfection." D.W. Stroock in Bulletin of the American Mathematical Society, 1980 "To call this work encyclopedic would not give an accurate picture of its content and style. Some parts read like a textbook, but others are more technical and contain relatively new results. ... The exposition is robust and explicit, as one has come to expect of the Russian tradition of mathematical writing. The set when completed will be an invaluable source of information and reference in this everexpanding field" K.L. Chung in American Scientist, 1977 "..., the subject has grown enormously since 1953, and there will never be a true successor to Doob's book, but Gihman and Skorohod's three volumes will, I think, occupy a rather similar position as an invaluable tool of reference for all probability theorists. ... The dominant impression is of the authors' mastery of their material, and of their confident insight into its underlying structure. ..." J.F.C. Kingman in Bulletin of the London Mathematical Society, 1977
Introduction to the theory of random processes by
I. I Gikhman(
Book
)
28 editions published between 1965 and 1996 in English and held by 635 WorldCat member libraries worldwide
28 editions published between 1965 and 1996 in English and held by 635 WorldCat member libraries worldwide
Studies in the theory of random processes by
A. V Skorokhod(
Book
)
26 editions published between 1965 and 1982 in English and held by 512 WorldCat member libraries worldwide
This text is devoted to the development of certain probabilistic methods in the specific field of stochastic differential equations and limit theorems for Markov processes. Specialists, researchers, and students in the field of probability will find it a source of important theorems as well as a remarkable amount of advanced material in compact form. The treatment begins by introducing the basic facts of the theory of random processes and constructing the auxiliary apparatus of stochastic integrals. All proofs are presented in full. Succeeding chapters explore the theory of stochastic differential equations, permitting the construction of a broad class of Markov processes on the basis of simple processes. The final chapters are devoted to various limit theorems connected with the convergence of a sequence of Markov chains to a Markov process with continuous time. Topics include the probability method of estimating how fast the sequence converges in the limit theorems and the precision of the limit theorems
26 editions published between 1965 and 1982 in English and held by 512 WorldCat member libraries worldwide
This text is devoted to the development of certain probabilistic methods in the specific field of stochastic differential equations and limit theorems for Markov processes. Specialists, researchers, and students in the field of probability will find it a source of important theorems as well as a remarkable amount of advanced material in compact form. The treatment begins by introducing the basic facts of the theory of random processes and constructing the auxiliary apparatus of stochastic integrals. All proofs are presented in full. Succeeding chapters explore the theory of stochastic differential equations, permitting the construction of a broad class of Markov processes on the basis of simple processes. The final chapters are devoted to various limit theorems connected with the convergence of a sequence of Markov chains to a Markov process with continuous time. Topics include the probability method of estimating how fast the sequence converges in the limit theorems and the precision of the limit theorems
Integration in Hilbert space by
A. V Skorokhod(
Book
)
27 editions published between 1974 and 1975 in 5 languages and held by 495 WorldCat member libraries worldwide
Integration in function spaces arose in probability theory when a gen eral theory of random processes was constructed. Here credit is cer tainly due to N. Wiener, who constructed a measure in function space, integralswith respect to which express the mean value of functionals of Brownian motion trajectories. Brownian trajectories had previously been considered as merely physical (rather than mathematical) phe nomena. A. N. Kolmogorov generalized Wiener's construction to allow one to establish the existence of a measure corresponding to an arbitrary random process. These investigations were the beginning of the development of the theory of stochastic processes. A considerable part of this theory involves the solution of problems in the theory of measures on function spaces in the specific language of stochastic pro cesses. For example, finding the properties of sample functions is connected with the problem of the existence of a measure on some space; certain problems in statistics reduce to the calculation of the density of one measure w. r. t. another one, and the study of transformations of random processes leads to the study of transformations of function spaces with measure. One must note that the language of probability theory tends to obscure the results obtained in these areas for mathematicians working in other fields. Another dir,ection leading to the study of integrals in function space is the theory and application of differential equations. A. N
27 editions published between 1974 and 1975 in 5 languages and held by 495 WorldCat member libraries worldwide
Integration in function spaces arose in probability theory when a gen eral theory of random processes was constructed. Here credit is cer tainly due to N. Wiener, who constructed a measure in function space, integralswith respect to which express the mean value of functionals of Brownian motion trajectories. Brownian trajectories had previously been considered as merely physical (rather than mathematical) phe nomena. A. N. Kolmogorov generalized Wiener's construction to allow one to establish the existence of a measure corresponding to an arbitrary random process. These investigations were the beginning of the development of the theory of stochastic processes. A considerable part of this theory involves the solution of problems in the theory of measures on function spaces in the specific language of stochastic pro cesses. For example, finding the properties of sample functions is connected with the problem of the existence of a measure on some space; certain problems in statistics reduce to the calculation of the density of one measure w. r. t. another one, and the study of transformations of random processes leads to the study of transformations of function spaces with measure. One must note that the language of probability theory tends to obscure the results obtained in these areas for mathematicians working in other fields. Another dir,ection leading to the study of integrals in function space is the theory and application of differential equations. A. N
Stochastic differential equations by
I. I Gikhman(
Book
)
18 editions published between 1972 and 2014 in 4 languages and held by 490 WorldCat member libraries worldwide
18 editions published between 1972 and 2014 in 4 languages and held by 490 WorldCat member libraries worldwide
Controlled stochastic processes by
I. I Gikhman(
Book
)
20 editions published between 1979 and 1980 in English and Undetermined and held by 357 WorldCat member libraries worldwide
The theory of controlled processes is one of the most recent mathematical theories to show very important applications in modern engineering, parti cularly for constructing automatic control systems, as well as for problems of economic control. However, actual systems subject to control do not admit a strictly deterministic analysis in view of random factors of various kinds which influence their behavior. Such factors include, for example, random noise occurring in the electrical system, variations in the supply and demand of commodities, fluctuations in the labor force in economics, and random failures of components on an automated line. The theory of con trolled processes takes the random nature of the behavior of a system into account. In such cases it is natural, when choosing a control strategy, to proceed from the average expected result, taking note of all the possible variants of the behavior of a controlled system. An extensive literature is devoted to various economic and engineering systems of control (some of these works are listed in the Bibliography). is no text which adequately covers the general However, as of now there mathematical theory of controlled processes. The authors ofthis monograph have attempted to fill this gap. In this volume the general theory of discreteparameter (time) controlled processes (Chapter 1) and those with continuoustime (Chapter 2), as well as the theory of controlled stochastic differential equations (Chapter 3), are presented
20 editions published between 1979 and 1980 in English and Undetermined and held by 357 WorldCat member libraries worldwide
The theory of controlled processes is one of the most recent mathematical theories to show very important applications in modern engineering, parti cularly for constructing automatic control systems, as well as for problems of economic control. However, actual systems subject to control do not admit a strictly deterministic analysis in view of random factors of various kinds which influence their behavior. Such factors include, for example, random noise occurring in the electrical system, variations in the supply and demand of commodities, fluctuations in the labor force in economics, and random failures of components on an automated line. The theory of con trolled processes takes the random nature of the behavior of a system into account. In such cases it is natural, when choosing a control strategy, to proceed from the average expected result, taking note of all the possible variants of the behavior of a controlled system. An extensive literature is devoted to various economic and engineering systems of control (some of these works are listed in the Bibliography). is no text which adequately covers the general However, as of now there mathematical theory of controlled processes. The authors ofthis monograph have attempted to fill this gap. In this volume the general theory of discreteparameter (time) controlled processes (Chapter 1) and those with continuoustime (Chapter 2), as well as the theory of controlled stochastic differential equations (Chapter 3), are presented
Asymptotic methods in the theory of stochastic differential equations by
A. V Skorokhod(
Book
)
12 editions published between 1989 and 2009 in English and Undetermined and held by 316 WorldCat member libraries worldwide
12 editions published between 1989 and 2009 in English and Undetermined and held by 316 WorldCat member libraries worldwide
Random linear operators by
A. V Skorokhod(
Book
)
16 editions published between 1983 and 2001 in English and Undetermined and held by 312 WorldCat member libraries worldwide
16 editions published between 1983 and 2001 in English and Undetermined and held by 312 WorldCat member libraries worldwide
Random perturbation methods with applications in science and engineering by
A. V Skorokhod(
Book
)
17 editions published between 2002 and 2013 in English and held by 271 WorldCat member libraries worldwide
As systems evolve, they are subjected to random operating environments. In addition, random errors occur in measurements of their outputs and in their design and fabrication where tolerances are not precisely met. This book develops methods for describing random dynamical systems, and it illustrates how the methods can be used in a variety of applications. The first half of the book concentrates on finding approximations to random processes using the methodologies of probability theory. The second half of the book derives approximations to solutions of various problems in mechanics, electronic circuits, population biology, and genetics. In each example, the underlying physical or biological phenomenon is described in terms of nonrandom models taken from the literature, and the impact of random noise on the solutions is investigated. The mathematical problems in these applicitons involve random pertubations of gradient systems, Hamiltonian systems, toroidal flows, Markov chains, difference equations, filters, and nonlinear renewal equations. The models are analyzed using the approximation methods described here and are visualized using MATLABbased computer simulations. This book will appeal to those researchers and graduate students in science and engineering who require tools to investigate stochastic systems
17 editions published between 2002 and 2013 in English and held by 271 WorldCat member libraries worldwide
As systems evolve, they are subjected to random operating environments. In addition, random errors occur in measurements of their outputs and in their design and fabrication where tolerances are not precisely met. This book develops methods for describing random dynamical systems, and it illustrates how the methods can be used in a variety of applications. The first half of the book concentrates on finding approximations to random processes using the methodologies of probability theory. The second half of the book derives approximations to solutions of various problems in mechanics, electronic circuits, population biology, and genetics. In each example, the underlying physical or biological phenomenon is described in terms of nonrandom models taken from the literature, and the impact of random noise on the solutions is investigated. The mathematical problems in these applicitons involve random pertubations of gradient systems, Hamiltonian systems, toroidal flows, Markov chains, difference equations, filters, and nonlinear renewal equations. The models are analyzed using the approximation methods described here and are visualized using MATLABbased computer simulations. This book will appeal to those researchers and graduate students in science and engineering who require tools to investigate stochastic systems
Stochastic equations for complex systems by
A. V Skorokhod(
Book
)
12 editions published in 1988 in English and held by 223 WorldCat member libraries worldwide
12 editions published in 1988 in English and held by 223 WorldCat member libraries worldwide
Random processes with independent increments by
A. V Skorokhod(
Book
)
15 editions published between 1966 and 1991 in English and Dutch and held by 219 WorldCat member libraries worldwide
15 editions published between 1966 and 1991 in English and Dutch and held by 219 WorldCat member libraries worldwide
Basic principles and applications of probability theory by
A. V Skorokhod(
Book
)
17 editions published between 2004 and 2008 in English and held by 184 WorldCat member libraries worldwide
"The book is an introduction to modern probability theory written by one of the famous experts in this area. Readers will learn the basic concepts of probability and its applications, preparing them for more advanced and specialized works."Jacket
17 editions published between 2004 and 2008 in English and held by 184 WorldCat member libraries worldwide
"The book is an introduction to modern probability theory written by one of the famous experts in this area. Readers will learn the basic concepts of probability and its applications, preparing them for more advanced and specialized works."Jacket
Stochastische Differentialgleichungen by
I. I Gikhman(
Book
)
10 editions published in 1971 in German and Undetermined and held by 136 WorldCat member libraries worldwide
10 editions published in 1971 in German and Undetermined and held by 136 WorldCat member libraries worldwide
The theory of Stochastic processes by
I. I Gikhman(
Book
)
24 editions published between 1975 and 2007 in English and held by 124 WorldCat member libraries worldwide
It was originally planned that the Theory of Stochastic Processes would consist of two volumes: the first to be devoted to general problems and the second to specific cJasses of random processes. It became apparent, however, that the amount of material related to specific problems of the theory could not possibly be incJuded in one volume. This is how the present third volume came into being. This voJume contains the theory of martingales, stochastic integrals, stochastic differential equations, diffusion, and continuous Markov processes. The theory of stochastic processes is an actively developing branch of mathe matics, and it would be an unreasonable and impossible task to attempt to encompass it in a single treatise (even a multivolume one). Therefore, the authors, guided by their own considerations concerning the relative importance of various results, naturally had to be selective in their choice of material. The authors are fully aware that such a selective process is not perfecL Even a number of topics that are, in the authors' opinion, of great importance could not be incJuded, for example, limit theorems for particular cJasses of random processes, the theory of random fields, conditional Markov processes, and information and statistics of random processes. With the publication of this last volume, we recall with gratitude oUf associates who assisted us in this endeavor, and express our sincere thanks to G. N. Sytaya, L. V. Lobanova, P. V. Boiko, N. F. Ryabova, N. A. Skorohod, V. V. Skorohod, N. I. Portenko, and L. I. Gab
24 editions published between 1975 and 2007 in English and held by 124 WorldCat member libraries worldwide
It was originally planned that the Theory of Stochastic Processes would consist of two volumes: the first to be devoted to general problems and the second to specific cJasses of random processes. It became apparent, however, that the amount of material related to specific problems of the theory could not possibly be incJuded in one volume. This is how the present third volume came into being. This voJume contains the theory of martingales, stochastic integrals, stochastic differential equations, diffusion, and continuous Markov processes. The theory of stochastic processes is an actively developing branch of mathe matics, and it would be an unreasonable and impossible task to attempt to encompass it in a single treatise (even a multivolume one). Therefore, the authors, guided by their own considerations concerning the relative importance of various results, naturally had to be selective in their choice of material. The authors are fully aware that such a selective process is not perfecL Even a number of topics that are, in the authors' opinion, of great importance could not be incJuded, for example, limit theorems for particular cJasses of random processes, the theory of random fields, conditional Markov processes, and information and statistics of random processes. With the publication of this last volume, we recall with gratitude oUf associates who assisted us in this endeavor, and express our sincere thanks to G. N. Sytaya, L. V. Lobanova, P. V. Boiko, N. F. Ryabova, N. A. Skorohod, V. V. Skorohod, N. I. Portenko, and L. I. Gab
Lectures on the theory of stochastic processes by
A. V Skorokhod(
Book
)
7 editions published in 1996 in English and held by 121 WorldCat member libraries worldwide
7 editions published in 1996 in English and held by 121 WorldCat member libraries worldwide
Introduction à la théorie des processus aléatoires by
I. I Gikhman(
Book
)
11 editions published between 1980 and 1986 in French and Italian and held by 83 WorldCat member libraries worldwide
11 editions published between 1980 and 1986 in French and Italian and held by 83 WorldCat member libraries worldwide
Sluchaĭnye prot︠s︡essy s nezavisimymi prirashchenii︠a︡mi by
A. V Skorokhod(
Book
)
8 editions published between 1964 and 1986 in Russian and English and held by 67 WorldCat member libraries worldwide
8 editions published between 1964 and 1986 in Russian and English and held by 67 WorldCat member libraries worldwide
Vvedenie v teorii︠u︡ sluchaĭnykh prot︠s︡essov by
I. I Gikhman(
Book
)
6 editions published between 1965 and 1977 in Russian and Undetermined and held by 51 WorldCat member libraries worldwide
6 editions published between 1965 and 1977 in Russian and Undetermined and held by 51 WorldCat member libraries worldwide
Exploring stochastic laws : Festschrift in honor of the 70th birthday of academician Vladimir Semenovich Korolyuk(
Book
)
5 editions published in 1995 in English and held by 43 WorldCat member libraries worldwide
5 editions published in 1995 in English and held by 43 WorldCat member libraries worldwide
Predelʹnye teoremy dli︠a︡ sluchaĭnykh bluzhdaniĭ by
A. V Skorokhod(
Book
)
3 editions published between 1970 and 1979 in Russian and held by 36 WorldCat member libraries worldwide
3 editions published between 1970 and 1979 in Russian and held by 36 WorldCat member libraries worldwide
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Related Identities
 Gikhman, I. I. (Iosif Ilʹich) 1918 Author
 Salehi, Habib
 Hoppensteadt, Frank C. (Frank Charles) 1938
 Prokhorov, I︠U︡. V. (I︠U︡riĭ Vasilʹevich) Editor
 Kotz, Samuel Translator
 Instytut matematyky (Akademii︠a︡ nauk Ukraïnsʹkoï RSR)
 Koroli︠u︡k, V. S. (Vladimir Semenovich) 1925 Honoree Editor
 Scripta Technica, Inc.
 Embarek, Djilali Other Translator
 Portenko, N. I. (Nikolaĭ Ivanovich) Author
Useful Links
Associated Subjects
Asymptotic expansions Control theory Differentiable dynamical systems Distribution (Probability theory) Functional analysis Hilbert space Integrals Integrals, Generalized Limit theorems (Probability theory) Linear operators Markov processes Mathematics Measure theory Numerical integration Perturbation (Mathematics) Probabilities Random operators Skorokhod, A. V.(Anatoliĭ Vladimirovich), Statistics Stochastic differential equations Stochastic processes
Alternative Names
Anatoli Skorochod ukrainischer Mathematiker
Anatoliy Skorokhod
Anatoliy Skorokhod Ukrainian mathematician
Skorochod, A. V. 19302011
Skorochod, A. W.
Skorochod, A. W. 1930
Skorochod, A. W. 19302011
Skorochod, Anatoliǐ Vladimirovich 19302011
Skorochod, Anatolij Vladimirovič
Skorochod, Anatolij Vladimirovič 19302011
Skorochod, Anatolij Vladimirovič. [t]
Skorohod, A.V.
Skorohod, A.V. 1930
Skorohod, A. V. 19302011
Skorohod, Anatolii Vladimirovich
Skorohod, Anatoliǐ Vladimirovich 19302011
Skorohod, Anatolij V. 19302011
Skorohod, Anatolij Vladimirovič.
Skorohod, Anatolij Vladimirovich
Skorokhod, A.
Skorokhod, A. V.
Skorokhod, A.V. 1930
Skorokhod, A. V. 19302011
Skorokhod, A. V. (Anatoliĭ Vladimirovich), 19302011
Skorokhod, A. W. 19302011
Skorokhod, Anatole V
Skorokhod, Anatole V. 19302011
Skorokhod, Anatoli V.
Skorokhod, Anatoli V. 19302011
Skorokhod, Anatoli Vladimirovitch
Skorokhod Anatoli Vladimirovitch 1930....
Skorokhod, Anatolii V. 19302011
Skorokhod, Anatoliĭ Vladimirovich
Skorokhod, Anatoliĭ Vladimirovich 1930
Skorokhod, Anatoliĭ Vladimirovich 19302011
Skorokhod, Anatoliy Volodymyrovych 19302011
Анатолій Володимирович Скороход советский математик
Скороход, А. В 19302011
Скороход, А. В. (Анатолий Владимирович), 19302011
Скороход, Анатолий Владимирович
Скороход, Анатолий Владимирович 1930...
Скороход, Анатолий Владимирович 19302011
Скороход Анатолій Володимирович
Скороход, Анатолій Володимирович 19302011
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