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From Irrevocably Modulated Filtrations to Dynamical Equations Over Random Networks

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  • Levent Ali Mengütürk

    (University College London)

Abstract

We develop a probabilistic information framework via what we call irrevocably modulated filtrations produced by non-invertible matrix-valued jump processes acting on multivariate observation processes carrying noisy signals. Under certain conditions, we provide dynamical representations of conditional expectation martingales in systems where signals from randomly changing information networks may get irreversibly amalgamated or switched-off over random time horizons. We apply the framework to scenarios where the flow of information goes through multiple modulations before reaching observing agents. This leads us to introduce a Lie-type operator as a morphism between spaces of sigma-algebras, which quantifies information discrepancy caused by different modulation sequences. As another example, we show how random graphs can be used to generate irrevocably modulated filtrations that lead to pure noise scenarios. Finally, we construct systems that exhibit gradual decay of additional sources of information through the choice of spectral radii of the modulators.

Suggested Citation

  • Levent Ali Mengütürk, 2023. "From Irrevocably Modulated Filtrations to Dynamical Equations Over Random Networks," Journal of Theoretical Probability, Springer, vol. 36(2), pages 845-875, June.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:2:d:10.1007_s10959-022-01201-0
    DOI: 10.1007/s10959-022-01201-0
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    References listed on IDEAS

    as
    1. Dorje C Brody, 2019. "Modelling election dynamics and the impact of disinformation," Papers 1904.12614, arXiv.org, revised Sep 2019.
    2. Hoyle, Edward & Mengütürk, Levent Ali, 2013. "Archimedean survival processes," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 1-15.
    3. Edward Hoyle & Levent Ali Menguturk, 2020. "Generalised Liouville Processes and their Properties," Papers 2003.11312, arXiv.org, revised May 2020.
    4. Edward Hoyle & Andrea Macrina & Levent Ali Mengütürk, 2020. "Modulated Information Flows In Financial Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(04), pages 1-35, June.
    5. Sottinen, Tommi & Yazigi, Adil, 2014. "Generalized Gaussian bridges," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3084-3105.
    6. Hoyle, Edward & Hughston, Lane P. & Macrina, Andrea, 2011. "Lévy random bridges and the modelling of financial information," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 856-884, April.
    7. Edward Hoyle & Andrea Macrina & Levent A. Menguturk, 2017. "Modulated Information Flows in Financial Markets," Papers 1708.06948, arXiv.org, revised May 2020.
    8. Dorje C. Brody & Lane P. Hughston & Andrea Macrina, 2008. "Information-Based Asset Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 107-142.
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