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-65%Studies in the Theory of Random Processes—
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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 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.
Reprint of the Addison-Wesley Publishing Co., Reading, Massachusetts, 1965 edition.
Translated from the Russian by Scripta Technica, Inc.
First published, in Russian--Kiev University Press, 1961.
First published in this translation: Addison-Wesley, 1965).
--In Adiwes International Series in Mathematics.
Includes Index, bibliography.
First Dover: (NY Dover, 1982)
2017: Dover reprint of Dover 1982, no changes
Stochastic Processes; Markov processes; Martingales; Stochastic integrals; Brownian motion; Stochastic equations; One-Dimensional Diffusion Processes; Independent random variables.First published, in Russian--Kiev University Press, 1961.
First published in this translation: Addison-Wesley, 1965).
--In Adiwes International Series in Mathematics.
Includes Index, bibliography.
First Dover: (NY Dover, 1982)
2017: Dover reprint of Dover 1982, no changes
Description
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 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.
Reprint of the Addison-Wesley Publishing Co., Reading, Massachusetts, 1965 edition.
Translated from the Russian by Scripta Technica, Inc.
First published, in Russian--Kiev University Press, 1961.
First published in this translation: Addison-Wesley, 1965).
--In Adiwes International Series in Mathematics.
Includes Index, bibliography.
First Dover: (NY Dover, 1982)
2017: Dover reprint of Dover 1982, no changes
Stochastic Processes; Markov processes; Martingales; Stochastic integrals; Brownian motion; Stochastic equations; One-Dimensional Diffusion Processes; Independent random variables.First published, in Russian--Kiev University Press, 1961.
First published in this translation: Addison-Wesley, 1965).
--In Adiwes International Series in Mathematics.
Includes Index, bibliography.
First Dover: (NY Dover, 1982)
2017: Dover reprint of Dover 1982, no changes
