Titel: Stochastic Processes
Autor/en: Kiyosi Ito
Lectures given at Aarhus University.
Herausgegeben von Ole E Barndorff-Nielsen, Ken-Iti Sato
Springer Berlin Heidelberg
12. März 2004 - gebunden - 248 Seiten
This is 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, today called the Levy-Ito decomposition, in a form close to Ito's original paper from 1942. 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.
0 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.
Kiyosi Itô was born on September 1915, in Kuwana, Japan. After his undergraduate and doctoral studies at Tokyo University, he was associate professor at Nagoya University before joining the faculty of Kyoto University in 1952. He has remained there ever since and is now Professor Emeritus, but has also spent several years at each of Stanford, Aarhus and Cornell Universities and the University of Minnesota. Itô's fundamental contributions to probability theory, especially the creation of stochastic differential and integral calculus and of excursion theory, form a cornerstone of this field. They have led to a profound understanding of the infinitesimal development of Markovian sample paths, and also of applied problems and phenomena associated with the planning, control and optimization of engineering and other random systems.
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)