Integrable Deformation of Gaussian Distribution and the Ornstein-Uhlenbeck Process |
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Authors: | Nakamura Yoshimasa |
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Institution: | (1) Applied Mathematics, [Doshisha University, Tanabe, Kyoto, 610-03, Japan. e-mail: naka@gandalf.doshisha.ac.jp |
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Abstract: | An integrable deformation of one-dimensional Gaussian distribution in terms of a continuous Moser hierarchy is described explicitly. Here the hierarchy governs the level dynamics of the semi-infinite Toda molecule. The action of the second-order flow is shown to be equivalent to that of the Ornstein–Uhlenbeck diffusion process. |
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Keywords: | integrable deformation Gaussian distribution Ornstein– Uhlenbeck diffuxion process Moser's dynamical system Toda molecule |
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