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Estimating sample paths of Gauss-Markov processes from noisy data

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  • Benjamin Davies

Abstract

I derive the pointwise conditional means and variances of an arbitrary Gauss-Markov process, given noisy observations of points on a sample path. These moments depend on the process's mean and covariance functions, and on the conditional moments of the sampled points. I study the Brownian motion and bridge as special cases.

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  • Benjamin Davies, 2024. "Estimating sample paths of Gauss-Markov processes from noisy data," Papers 2404.00784, arXiv.org.
    • Handle: RePEc:arx:papers:2404.00784
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    References listed on IDEAS

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    1. Benjamin Davies, 2024. "Learning about a changing state," Papers 2401.03607, arXiv.org.
    2. Steven Callander, 2011. "Searching and Learning by Trial and Error," American Economic Review, American Economic Association, vol. 101(6), pages 2277-2308, October.
    3. Christoph Carnehl & Johannes Schneider, 2021. "A Quest for Knowledge," Papers 2102.13434, arXiv.org, revised Jul 2024.
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