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

Nobuyuki Ikeda; Setsuo Taniguchi

doi:10.1016/j.spa.2010.01.009

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

Nobuyuki Ikeda, Setsuo Taniguchi

Division for Theoretical Natural Science

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	605-621
Number of pages	17
Journal	Stochastic Processes and their Applications
Volume	120
Issue number	5
DOIs	https://doi.org/10.1016/j.spa.2010.01.009
Publication status	Published - May 2010

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1016/j.spa.2010.01.009

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abstract = "Among Professor Kiyosi It{\^o}'s achievements, there is the It{\^o}-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.",

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

Abstract

All Science Journal Classification (ASJC) codes

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