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ファイル | 記述 | サイズ | フォーマット | |
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B59-06.pdf | 5.25 MB | Adobe PDF | 見る/開く |
タイトル: | Central limit theorem for finite and infinite dimensional diffusions in ergodic environments (Stochastic Analysis on Large Scale Interacting Systems) |
著者: | Xu, Lu |
キーワード: | 60F05 60H15 60K37 random environment homogenization diffusion process stochastic heat equation |
発行日: | Jul-2016 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
誌名: | 数理解析研究所講究録別冊 |
巻: | B59 |
開始ページ: | 57 |
終了ページ: | 68 |
抄録: | In this article, we introduce a central limit theorem for the solution to a 1-dimensional stochastic heat equation with a random, ergodic non-linear term. Since it can be viewed as an infinite dimensional diffusion in random environment, we first summarize the ideas in the classical central limit theorem for finite dimensional diffusion in random environment, based on [8, x9]. Afterward, we illustrate the strategy to extend these ideas to stochastic heat equations, and explain the main differences between finite and infinite dimensional models. Due to our result, a central limit theorem in L1 sense with respect to the randomness of the environment holds and the limit distribution is a centered Gaussian law, whose covariance operator is explicitly described. Moreover, it concentrates only on the space of constant functions. |
記述: | "Stochastic Analysis on Large Scale Interacting Systems". October 26~29, 2015. edited by Ryoki Fukushima, Tadahisa Funaki, Yukio Nagahata, Makoto Nakashima, Hirofumi Osada and Yoshiki Otobe. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. |
著作権等: | © 2016 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. |
URI: | http://hdl.handle.net/2433/243593 |
出現コレクション: | B59 Stochastic Analysis on Large Scale Interacting Systems |
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