Skorokhod, A. V. (Anatoliĭ Vladimirovich) 19302011
Overview
Works:  179 works in 696 publications in 6 languages and 7,769 library holdings 

Roles:  Author, Editor, Adapter, ed 
Classifications:  QA274, 519.2 
Publication Timeline
.
Most widely held works by
A. V Skorokhod
Introduction to the theory of random processes by
I. I Gikhman(
Book
)
32 editions published between 1965 and 1996 in English and held by 642 WorldCat member libraries worldwide
32 editions published between 1965 and 1996 in English and held by 642 WorldCat member libraries worldwide
Integration in Hilbert space by
A. V Skorokhod(
Book
)
27 editions published between 1974 and 2012 in 3 languages and held by 509 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 2012 in 3 languages and held by 509 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 3 languages and held by 501 WorldCat member libraries worldwide
18 editions published between 1972 and 2014 in 3 languages and held by 501 WorldCat member libraries worldwide
Studies in the theory of random processes by
A. V Skorokhod(
Book
)
20 editions published between 1965 and 2014 in English and held by 498 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
20 editions published between 1965 and 2014 in English and held by 498 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
The theory of stochastic processes by
I. I Gikhman(
Book
)
11 editions published between 1973 and 2004 in English and held by 453 WorldCat member libraries worldwide
11 editions published between 1973 and 2004 in English and held by 453 WorldCat member libraries worldwide
The theory of stochastic processes by
I. I Gikhman(
Book
)
82 editions published between 197 and 2007 in 3 languages and held by 374 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
82 editions published between 197 and 2007 in 3 languages and held by 374 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
Controlled stochastic processes by
I. I Gikhman(
Book
)
18 editions published between 1979 and 1980 in English and Undetermined and held by 351 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
18 editions published between 1979 and 1980 in English and Undetermined and held by 351 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
Random linear operators by
A. V Skorokhod(
Book
)
17 editions published between 1983 and 2001 in English and Undetermined and held by 320 WorldCat member libraries worldwide
17 editions published between 1983 and 2001 in English and Undetermined and held by 320 WorldCat member libraries worldwide
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 320 WorldCat member libraries worldwide
12 editions published between 1989 and 2009 in English and Undetermined and held by 320 WorldCat member libraries worldwide
Random perturbation methods with applications in science and engineering by
A. V Skorokhod(
Book
)
20 editions published between 2002 and 2013 in English and held by 273 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
20 editions published between 2002 and 2013 in English and held by 273 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 227 WorldCat member libraries worldwide
12 editions published in 1988 in English and held by 227 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 220 WorldCat member libraries worldwide
The book deals with the theory of random process with independent increment  one of the most important branches of randomprocess theory. This represents the first collection of numerous important results obtained in the study of random processes with independent increments. These results have been scattered through various articles. The book will be of interest both for specialists in probability theory working in the field of random processes, as well as for those studying the theory of random processes and concerned with its applications in various scientific fields. (Author)
15 editions published between 1966 and 1991 in English and Dutch and held by 220 WorldCat member libraries worldwide
The book deals with the theory of random process with independent increment  one of the most important branches of randomprocess theory. This represents the first collection of numerous important results obtained in the study of random processes with independent increments. These results have been scattered through various articles. The book will be of interest both for specialists in probability theory working in the field of random processes, as well as for those studying the theory of random processes and concerned with its applications in various scientific fields. (Author)
Probability theory; basic concepts, limit theorems, random processes by
A. V Skorokhod(
Book
)
21 editions published between 2004 and 2008 in English and held by 211 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
21 editions published between 2004 and 2008 in English and held by 211 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
The theory of stochastic processes by
I. I Gikhman(
Book
)
37 editions published between 1974 and 2004 in English and German and held by 170 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
37 editions published between 1974 and 2004 in English and German and held by 170 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
Stochastische Differentialgleichungen by
I. I Gikhman(
Book
)
11 editions published in 1971 in German and Undetermined and held by 155 WorldCat member libraries worldwide
11 editions published in 1971 in German and Undetermined and held by 155 WorldCat member libraries worldwide
Lectures on the theory of stochastic processes by
A. V Skorokhod(
Book
)
8 editions published in 1996 in English and held by 122 WorldCat member libraries worldwide
8 editions published in 1996 in English and held by 122 WorldCat member libraries worldwide
Introduction à la théorie des processus aléatoires by
I. I Gikhman(
Book
)
14 editions published between 1980 and 1986 in 3 languages and held by 93 WorldCat member libraries worldwide
14 editions published between 1980 and 1986 in 3 languages and held by 93 WorldCat member libraries worldwide
Sluchaĭnye prot︠s︡essy s nezavisimymi prirashchenii︠a︡mi by
A. V Skorokhod(
Book
)
7 editions published between 1964 and 1986 in Russian and English and held by 66 WorldCat member libraries worldwide
7 editions published between 1964 and 1986 in Russian and English and held by 66 WorldCat member libraries worldwide
Exploring stochastic laws : Festschrift in honor of the 70th birthday of academician Vladimir Semenovich Korolyuk(
Book
)
6 editions published in 1995 in English and held by 44 WorldCat member libraries worldwide
6 editions published in 1995 in English and held by 44 WorldCat member libraries worldwide
Predelʹnye teoremy dli︠a︡ sluchaĭnykh bluzhdaniĭ by
A. V Skorokhod(
Book
)
5 editions published between 1970 and 1979 in Russian and held by 38 WorldCat member libraries worldwide
5 editions published between 1970 and 1979 in Russian and held by 38 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
 Seckler, B. D.
Useful Links
Associated Subjects
Asymptotic expansions Control theory Differentiable dynamical systems Differential equations 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 matematico ucraino
Anatoliy Skorokhod Ukrainian mathematician
Anatoliy Skorokhod wiskundige uit Oekraïne (19302011)
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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