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On concentration properties of partially observed chaotic systems

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Title: On concentration properties of partially observed chaotic systems
Authors: Paulin, D
Jasra, A
Crisan, D
Beskos, A
Item Type: Journal Article
Abstract: In this paper we present results on the concentration properties of the smoothing and filtering distributions of some partially observed chaotic dynamical systems. We show that, rather surprisingly, for the geometric model of the Lorenz equations, as well as some other chaotic dynamical systems, the smoothing and filtering distributions do not concentrate around the true position of the signal, as the number of observations tends to ∞. Instead, under various assumptions on the observation noise, we show that the expected value of the diameter of the support of the smoothing and filtering distributions remains lower bounded by a constant multiplied by the standard deviation of the noise, independently of the number of observations. Conversely, under rather general conditions, the diameter of the support of the smoothing and filtering distributions are upper bounded by a constant multiplied by the standard deviation of the noise. To some extent, applications to the three-dimensional Lorenz 63 model and to the Lorenz 96 model of arbitrarily large dimension are considered.
Issue Date: 1-Jun-2018
Date of Acceptance: 1-Jun-2018
URI: http://hdl.handle.net/10044/1/62979
DOI: https://dx.doi.org/10.1017/apr.2018.21
ISSN: 0001-8678
Start Page: 440
End Page: 479
Journal / Book Title: Advances in Applied Probability
Volume: 50
Issue: 2
Copyright Statement: © 2018 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Sponsor/Funder: Engineering and Physical Sciences Research Council
Funder's Grant Number: EP/N023781/1
Keywords: 0102 Applied Mathematics
0104 Statistics
Statistics & Probability
Publication Status: Published
Online Publication Date: 2018-07-26
Appears in Collections:Pure Mathematics
Mathematics



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