Stochastic Processes

by Kiyoshi Itō

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 Lévy-Itô decomposition, in a form close to Itô'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.

233 pages, Paperback

First published December 1, 1984

About the author

Professor Kiyosi Itô is one of the most distinguished probability theorists in the world. He is the creator of a branch of mathematics that deals with stochastics and probabilities, now known as Itō calculus in his honour, and one of its main tools is the stochastic integral, also known as Itō integral. This calculus plays a fundamental role in modern financial mathematics.

Itō died in Kyoto, Japan, in 2008. He was 93 years old.