Japanese Journal of Mathematics

, Volume 2, Issue 1, pp 45–53 | Cite as

On the works of Kiyosi Itô and stochastic analysis

Special Feature: Award of the 1st Gauss Prize to K. Ito


A common feature that can be consistently found in the works of Professor Kiyosi Itô is a leap from the analysis in distribution family level toward the analysis and synthesis in sample paths level, which has turned analytic descriptions into thoroughly stochastic ones.

Keywords and phrases:

Brownian motion Lévy–Itô decomposition Itô integral Itô formula stochastic differential equation Wiener–Itô decomposition one-dimensional diffusion excursions stochastic geometry stochastic control stochastic finance 

Mathematics Subject Classification (2000):



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Copyright information

© The Mathematical Society of Japan and Springer 2007

Authors and Affiliations

  1. 1.Osaka UniversityOsakaJapan

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