Oxley, W. and Kim, E.-J. (2018) Scalings and fractals in information geometry: Ornstein–Uhlenbeck processes. Journal of Statistical Mechanics: Theory and Experiment , 2018. 113401. ISSN 1742-5468
Abstract
We propose a new methodology to understand a stochastic process from the perspective of information geometry by investigating power-law scaling and fractals in the evolution of information. Specifically, we employ the Ornstein–Uhlenbeck process where an initial probability density function (PDF) with a given width and mean value y 0 relaxes into a stationary PDF with a width epsilon, set by the strength of a stochastic noise. By utilizing the information length which quantifies the accumulative information change, we investigate the scaling of with epsilon. When , the movement of a PDF leads to a robust power-law scaling with the fractal dimension . In general when , is possible in the limit of a large time when the movement of a PDF is a main process for information change (e.g. ). We discuss the physical meaning of different scalings due to PDF movement, diffusion and entropy change as well as implications of our finding for understanding a main process responsible for the evolution of information.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 IOP Publishing Ltd and SISSA Medialab srl. This is an author produced version of a paper subsequently published in Journal of Statistical Mechanics: Theory and Experiment. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Stochastic processes |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 19 Nov 2018 13:00 |
Last Modified: | 15 Nov 2019 01:56 |
Published Version: | https://doi.org/10.1088/1742-5468/aae851 |
Status: | Published |
Publisher: | IOP Publishing |
Refereed: | Yes |
Identification Number: | 10.1088/1742-5468/aae851 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:138738 |