eprintid: 14155 rev_number: 7 eprint_status: archive userid: 5 dir: disk0/00/01/41/55 datestamp: 2016-12-14 12:25:10 lastmod: 2021-08-27 17:41:44 status_changed: 2016-12-14 12:25:10 type: book_section metadata_visibility: show item_issues_count: 1 creators_name: Takeuchi, Y. creators_id: AL1725 title: On the decompositions of observations with non-Gaussian additive noise and their innovations processes ispublished: pub divisions: prog_dyn abstract: This paper is concerned with information structure of the observation with additive non-Gaussian noise under the assumption that the noise belongs to a class of continuous martingales. It is known that such an observation is decomposed into a process with additive Gaussian noise and the quadratic covariation process of the additive noise. It is also known that the innovations process is decomposed into a standard Brownian motion process and the quadratic covariation process. In this paper, a number of sufficient conditions are obtained for the observation to have the information structure such that the information in the quadratic covariation process is not contained in the additive Gaussian part of the observation and/or the Brownian motion part of the innovation process. date: 1990 date_type: published publisher: Springer Berlin Heidelberg id_number: 10.1007/BFb0120047 creators_browse_id: 2766 full_text_status: none series: Lecture Notes in Control and Information Sciences volume: 144 place_of_pub: Germany pagerange: 248-257 refereed: TRUE isbn: 978-3-540-47085-4 book_title: Analysis and Optimization of Systes editors_name: Bensoussan, A. editors_name: Lions, J.L. coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/bookPart citation: Takeuchi, Y. (1990). On the decompositions of observations with non-Gaussian additive noise and their innovations processes. In: Analysis and Optimization of Systes. Eds. Bensoussan, A. & Lions, J.L., pp. 248-257 Germany: Springer Berlin Heidelberg. ISBN 978-3-540-47085-4 10.1007/BFb0120047 .