Japanese Journal of Mathematics

, Volume 2, Issue 1, pp 137–143 | Cite as

How K. Itô revolutionized the study of stochastic processes

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

Abstract.

The main facts of K. Itô’s stochastic integration as well as excursion theory are presented, together with a number of applications.

Keywords and phrases:

stochastic calculus excursion theory enlargement of filtration 

Mathematics Subject Classification (2000):

60G07 60G44 60G51 60H05 60J65 

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General references to K.Itô’s works

  1. 1.
    K. Itô, Selected Papers (with an Introduction by D. Stroock and S. Varadlian), Springer, 1987.Google Scholar
  2. 2.
    N. Ikeda, S.Watanabe, M. Fukushima and H. Kunita (eds.), Itô’s Stochastic Calculus and Probability Theory, Springer, 1996.Google Scholar
  3. 3.
    P. Salminen, P. Vallois, and M. Yor, On the excursion theory for linear diffusions. Japan. J. Math., 2 (2007), 97–127.Google Scholar
  4. 4.
    M. Yor, Comment K.Itô a révolutionné l’étude des processus stochastiques. Gaz. Math., 111 (2007), 51-56.Google Scholar

Copyright information

© The Mathematical Society of Japan and Springer 2007

Authors and Affiliations

  1. 1.Laboratoire de Probabilités et Modèles AléatoiresUniversités Paris VI et VIIParis Cedex 05France
  2. 2.Institut Universitaire de FranceParisFrance

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