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Stochastic Processes : Lectures Given at Aarhus University by Kiyosi Ito (2004, Hardcover)
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Stochastic Processes : Lectures Given at Aarhus University, Hardcover by Sato, Kenichi (EDT); Ito, Kiyosi; Barndorff-Nielsen, O. E., ISBN 3540204822, ISBN-13 9783540204824, Brand New, Free shipping in the US This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes. It gives a thorough treatment of the decomposition of paths of processes with independent increments (the Lévy-Itô decomposition). It also contains a detailed treatment of time-homogeneous Markov processes from the viewpoint of probability measures on path space. In addition, 70 exercises and their complete solutions are included.
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About this product
Product Identifiers
PublisherSpringer Berlin / Heidelberg
ISBN-103540204822
ISBN-139783540204824
eBay Product ID (ePID)30515657
Product Key Features
Number of PagesXii, 236 Pages
LanguageEnglish
Publication NameStochastic Processes : Lectures Given at Aarhus University
SubjectProbability & Statistics / Stochastic Processes, Probability & Statistics / General
Publication Year2004
TypeTextbook
AuthorKiyosi Ito
Subject AreaMathematics
FormatHardcover
Dimensions
Item Height0.3 in
Item Weight41.3 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2004-044984
ReviewsFrom the reviews:"The book can be recommended as a fine introduction to such important branches of stochastic process theory as the theories of processes with independent increments and of Markov processes. It will be a valuable acquisition for any mathematical library. The text of the book has been carefully prepared by the editors … ." (M.G. Shur, Mathematical Reviews, 2005e)"The book under review is in fact an advanced text suitable for graduate students and based around two topics-the structure of additive processes … and the basic theory of Markov processes, which generalises Markov chains to continuous time and fairly general state spaces. … a nice introduction to Markov processes making extensive use of semigroup techniques. … The book concludes with a number of exercises accompanied by worked solutions." (David Applebaum, The Mathematical Gazette, March, 2005), From the reviews: "The book can be recommended as a fine introduction to such important branches of stochastic process theory as the theories of processes with independent increments and of Markov processes. It will be a valuable acquisition for any mathematical library. The text of the book has been carefully prepared by the editors 'e¦ ." (M.G. Shur, Mathematical Reviews, 2005e) "The book under review is in fact an advanced text suitable for graduate students and based around two topics-the structure of additive processes 'e¦ and the basic theory of Markov processes, which generalises Markov chains to continuous time and fairly general state spaces. 'e¦ a nice introduction to Markov processes making extensive use of semigroup techniques. 'e¦ The book concludes with a number of exercises accompanied by worked solutions." (David Applebaum, The Mathematical Gazette, March, 2005), From the reviews: "The book can be recommended as a fine introduction to such important branches of stochastic process theory as the theories of processes with independent increments and of Markov processes. It will be a valuable acquisition for any mathematical library. The text of the book has been carefully prepared by the editors ... ." (M.G. Shur, Mathematical Reviews, 2005e) "The book under review is in fact an advanced text suitable for graduate students and based around two topics-the structure of additive processes ... and the basic theory of Markov processes, which generalises Markov chains to continuous time and fairly general state spaces. ... a nice introduction to Markov processes making extensive use of semigroup techniques. ... The book concludes with a number of exercises accompanied by worked solutions." (David Applebaum, The Mathematical Gazette, March, 2005), From the reviews: "The book can be recommended as a fine introduction to such important branches of stochastic process theory as the theories of processes with independent increments and of Markov processes. It will be a valuable acquisition for any mathematical library. The text of the book has been carefully prepared by the editors … ." (M.G. Shur, Mathematical Reviews, 2005e) "The book under review is in fact an advanced text suitable for graduate students and based around two topics-the structure of additive processes … and the basic theory of Markov processes, which generalises Markov chains to continuous time and fairly general state spaces. … a nice introduction to Markov processes making extensive use of semigroup techniques. … The book concludes with a number of exercises accompanied by worked solutions." (David Applebaum, The Mathematical Gazette, March, 2005), From the reviews: "The book can be recommended as a fine introduction to such important branches of stochastic process theory as the theories of processes with independent increments and of Markov processes. It will be a valuable acquisition for any mathematical library. The text of the book has been carefully prepared by the editors a? ." (M.G. Shur, Mathematical Reviews, 2005e) "The book under review is in fact an advanced text suitable for graduate students and based around two topics-the structure of additive processes a? and the basic theory of Markov processes, which generalises Markov chains to continuous time and fairly general state spaces. a? a nice introduction to Markov processes making extensive use of semigroup techniques. a? The book concludes with a number of exercises accompanied by worked solutions." (David Applebaum, The Mathematical Gazette, March, 2005)
Number of Volumes1 vol.
IllustratedYes
Table Of Content0 Preliminaries.- 1 Additive Processes (Processes with Independent Increments).- 2 Markov Processes.- Exercises.- E.0 Chapter 0.- E.1 Chapter 1.- E.2 Chapter 2.- Appendix: Solutions of Exercises.- A.0 Chapter 0.- A.1 Chapter 1.- A.2 Chapter 2.
SynopsisThe volume Stochastic Processes by K. It was published as No. 16 of Lecture Notes Series from Mathematics Institute, Aarhus University in August, 1969, based on Lectures given at that Institute during the academie year 1968- 1969. The volume was as thick as 3.5 cm., mimeographed from typewritten manuscript and has been out of print for many years. Since its appearance, it has served, for those abIe to obtain one of the relatively few copies available, as a highly readable introduetion to basic parts of the theories of additive processes (processes with independent increments) and of Markov processes. It contains, in particular, a clear and detailed exposition of the L vy-It decomposition of additive processes. Encouraged by Professor It we have edited the volume in the present book form, amending the text in a number of places and attaching many footnotes. We have also prepared an index. Chapter 0 is for preliminaries. Here centralized sums of independent ran- dom variables are treated using the dispersion as a main tooI. L vy's form of characteristic functions of infinitely divisible distributions and basic proper- ties of martingales are given. Chapter 1 is analysis of additive processes. A fundamental structure the- orem describes the decomposition of sample functions of additive processes, known today as the L vy-It decomposition. This is thoroughly treated, as- suming no continuity property in time, in a form close to the original 1942 paper of It , which gave rigorous expression to L vy's intuitive understanding of path behavior., A readily accessible introduction to the theory of stochastic processes with emphasis on processes with independent increments and Markov processes. After preliminaries on infinitely divisible distributions and martingales, Chapter 1 gives a thorough treatment of the decomposition of paths of processes with independent increments. Chapter 2 contains a detailed treatment of time-homogeneous Markov processes from the viewpoint of probability measures on path space. Two separate Sections present about 70 exercises and their complete solutions. The text and exercises are carefully edited and footnoted, while retaining the style of the original lecture notes from Aarhus University., This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes. It gives a thorough treatment of the decomposition of paths of processes with independent increments (the Lèvy-Ito decomposition). It also contains a detailed treatment of time-homogeneous Markov processes from the viewpoint of probability measures on path space. In addition, 70 exercises and their complete solutions are included., The volume Stochastic Processes by K. Itö was published as No. 16 of Lecture Notes Series from Mathematics Institute, Aarhus University in August, 1969, based on Lectures given at that Institute during the academie year 1968 1969. The volume was as thick as 3.5 cm., mimeographed from typewritten manuscript and has been out of print for many years. Since its appearance, it has served, for those abIe to obtain one of the relatively few copies available, as a highly readable introduetion to basic parts of the theories of additive processes (processes with independent increments) and of Markov processes. It contains, in particular, a clear and detailed exposition of the Lévy-It ö decomposition of additive processes. Encouraged by Professor It ó we have edited the volume in the present book form, amending the text in a number of places and attaching many footnotes. We have also prepared an index. Chapter 0 is for preliminaries. Here centralized sums of independent ran dom variables are treated using the dispersion as a main tooI. Lévy's form of characteristic functions of infinitely divisible distributions and basic proper ties of martingales are given. Chapter 1 is analysis of additive processes. A fundamental structure the orem describes the decomposition of sample functions of additive processes, known today as the Lévy-Itó decomposition. This is thoroughly treated, as suming no continuity property in time, in a form close to the original 1942 paper of Itó, which gave rigorous expression to Lévy's intuitive understanding of path behavior.
LC Classification NumberQA273.A1-274.9
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