Filtered data based estimators for stochastic processes driven by colored noise
File(s)
Accepted version
Author(s)
Pavliotis, Grigorios A
Reich, Sebastian
Zanoni, Andrea
Type
Journal Article
Abstract
We consider the problem of estimating unknown parameters in stochastic differential equations driven by colored noise, which we model as a sequence of Gaussian stationary processes with decreasing correlation time. We aim to infer parameters in the limit equation, driven by white noise, given observations of the colored noise dynamics. We consider both the maximum likelihood and the stochastic gradient descent in continuous time estimators, and we propose to modify them by including filtered data. We provide a convergence analysis for our estimators showing their asymptotic unbiasedness in a general setting and asymptotic normality under a simplified scenario.
Date Issued
2025-03
Date Acceptance
2024-12-16
Citation
Stochastic Processes and their Applications, 2025, 181
ISSN
0304-4149
Publisher
Elsevier
Journal / Book Title
Stochastic Processes and their Applications
Volume
181
Copyright Statement
Copyright © 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Identifier
https://doi.org/10.1016/j.spa.2024.104558
Publication Status
Published
Article Number
104558
Date Publish Online
2024-12-24