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On the equations of stationary processes with divergent diffusion coefficients
| Title: | On the equations of stationary processes with divergent diffusion coefficients |
| Authors: | Inoue, Akihiko Browse this author |
| Issue Date: | 1993 |
| Publisher: | Faculty of Science, The University of Tokyo |
| Journal Title: | Journal of the Faculty of Science. University of Tokyo. Section IA. Mathematics |
| Volume: | 40 |
| Start Page: | 307 |
| End Page: | 336 |
| Abstract: | We investigate a class of Langevin equations with delay. The random noises in the equations are adopted so that they are in accordance with linear response theory in statistical physics. We prove that every purely nondetermistic, stationary Gaussian process with divergent diffusion coefficients as well as reflection positivity is characterized as the unique solution of one of such equations. This extends the results of Okabe to processes with divergent diffusion coefficients. A correspondence between the decays of the delay coefficient of the equation and the correlation function of the solution is obtained. We see that it is of different type from the case diffusion coefficients. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/20096 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 井上 昭彦
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