The Itô-Nisio theorem, quadratic Wiener functionals, and 1-solitons

Nobuyuki Ikeda, Setsuo Taniguchi

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


Among Professor Kiyosi Itô's achievements, there is the Itô-Nisio theorem, a completely general theorem relative to the Fourier series decomposition of Brownian motion. In this paper, some of its applications will be reviewed, and new applications to 1-soliton solutions to the Korteweg-de Vries (KdV for short) equation and Eulerian polynomials will be given.

Original languageEnglish
Pages (from-to)605-621
Number of pages17
JournalStochastic Processes and their Applications
Issue number5
Publication statusPublished - May 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics


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