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Symposium in Honor of Kiyosi Itô: Stochastic Analysis and Its Impact in Mathematics and Science

(10 - 11 Jul 2008)

... Jointly organized with Research Institute for Mathematical Sciences, Kyoto

 Organizing Committee

Co-Chairs

  • Hans Föllmer (Humboldt-University of Berlin)
  • Masatoshi Fukushima (Osaka University)

Members

  • Edwin Perkins (University of British Columbia)
  • Yoichiro Takahashi (Research Institute for Mathematical Sciences, Kyoto)
     

 Invited Speakers

  • Alain Bensoussan, University of Texas at Dallas
  • Donald Dawson, Carleton University
  • Masatoshi Fukushima, Osaka University
  • Shigeo Kusuoka, University of Tokyo
  • Terry Lyons, University of Oxford
  • Shinzo Watanabe, Kyoto University
  • Marc Yor, Université Paris VI

 Overview

Kiyosi Itô has made great contributions to the advancement of the mathematical sciences by laying the foundations of the theory of stochastic differential equations and of stochastic integration in 1942. He has also played a leading role in the subsequent development of these areas into a core chapter in modern probability theory, known as stochastic analysis.

Since the early 1950s the theory of stochastic differential equations has been gaining new perspectives through interactions with various branches of mathematics, including partial differential equations, potential theory, harmonic integrals, differential geometry, and harmonic analysis. However, this theory has wound up reaching far beyond the confines of mathematics. Itô’s theory of stochastic differential equations and the corresponding extension of classical calculus to highly irregular curves such as Brownian motion paths, now known as the "Itô calculus", are indispensable tools in analyzing random phenomena in fields as diverse as physics, biology, economics, and engineering.

The research on filtering initiated by R. Kalman could not have developed to its current stage without stochastic differential equations. In mathematical finance, in particular, in the research of F. Black, R. Merton and M. Scholes, for which Merton and Scholes received the 1997 Nobel Prize in Economics, stochastic differential equations and "Itô's formula" play crucial roles.

Itô has made significant contributions to many other topics as well, such as the Wiener- Itô chaos decomposition, one-dimensional diffusion processes, excursion theory for Markov processes, and infinite-dimensional diffusion processes. Itô’s work in stochastic analysis, along with the central role he has played in its subsequent development, typifies the twentieth-century mathematical sciences — having mathematical depth and strong interaction with a wide range of areas.

Itô was elected as a member of the Japan Academy of Sciences in 1991 and as a foreign member of the Académie des Sciences of France in 1989 and of the US Academy of Sciences in 1998. He has received many prizes which include the Japan Academy Prize (1978), the Wolf Prize (1987) and the Kyoto Prize (1998). He is also the recipient of the first Carl Friedrich Gauss Prize, awarded at the International Congress of Mathematicians at Madrid in 2006. He has also been conferred honorary degrees by Université Paris VI (1981), ETH Zürich (1987), and the University of Warwick (1992).

The objective of the symposium is to gather together leading mathematicians and scientists to deliver expository lectures on Itô's work, the historical development of stochastic analysis, and the influence and impact of stochastic analysis in various branches of mathematics and science. It will be aimed at mathematicians and scientists in general.

 Venue

 Schedule


Thursday, 10 Jul 2008

08:50am - 09:10am

Registration

09:10am - 09:30am

Opening remarks by:
Louis Chen, Institute for Mathematical Sciences
Edwin Perkins, University of British Columbia, Canada
Message from Professor Kiyosi Itô read by:
Masatoshi Fukushima, Osaka University, Japan

Presentation of gift to:
Masatoshi Fukushima representing Professor Itô

09:30am - 10:30am

On Itô's one point extensions of Markov processes (PDF)
Masatoshi Fukushima, Osaka University

10:30am - 11:00am

--- Coffee Break ---

11:00am - 12:00nn

Infinite dimensional affine processes (PDF)
Alain Bensoussan, University of Texas at Dallas

12:00nn - 02:00pm

--- Lunch Break ---

02:00pm - 03:00pm

Malliavin calculus and computational finance (PDF)
Shigeo Kusuoka, University of Tokyo

03:00pm - 03:30pm

--- Coffee Break ---

03:30pm - 04:30pm

Generalized black-Scholes formulae: the last passage time viewpoint
Marc Yor, Université Paris VI

End of day 1

Friday, 11 Jul 2008

09:20am - 09:30am

Registration

09:30am - 10:30am

Theory of Stochastic differential equations - an overview and examples (PDF1, PDF2)
Shinzo Watanabe, Kyoto University

10:30am - 11:00am

--- Coffee Break ---

11:00am - 12:00nn

Stochastic analysis in genetics and population modelling
Donald Dawson, Carleton University

12:00nn - 02:00pm

--- Lunch Break ---

02:00pm - 03:00pm

Rough paths
Terry Lyons, University of Oxford

03:00pm - 03:30pm

Video of presentation of Gauss Prize to Kiyosi Itô by IMU President John Ball and photographs about Kiyosi Itô

End of day 2

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