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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modelling and Simulation
- Applied Mathematics