Overview
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.
Full Product Details
Author: Kiyosi Ito ,
Ole E Barndorff-Nielsen ,
Ken-iti Sato
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: Softcover reprint of hardcover 1st ed. 2004
Dimensions:
Width: 15.50cm
, Height: 1.30cm
, Length: 23.50cm
Weight: 0.454kg
ISBN: 9783642058059
ISBN 10: 3642058051
Pages: 236
Publication Date: 30 November 2010
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: In Print
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Reviews
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 ... . (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)
