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Article

The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise

Department of Mathematics, Faculty of Chemical Engineering, University of Chemistry and Technology Prague, 16628 Prague, Czech Republic
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Mathematics 2020, 8(10), 1766; https://doi.org/10.3390/math8101766
Received: 10 September 2020 / Revised: 4 October 2020 / Accepted: 6 October 2020 / Published: 13 October 2020
(This article belongs to the Special Issue Random Processes on Graphs)
In the present paper, we study the problem of estimating a drift parameter in stochastic evolution equations on graphs. We focus on equations driven by fractional Brownian motions, which are particularly useful e.g., in biology or neuroscience. We derive a novel estimator (the combined estimator) and prove its strong consistency in the long-span asymptotic regime with a discrete-time sampling scheme. The promising performance of the combined estimator for finite samples is examined under various scenarios by Monte Carlo simulations. View Full-Text
Keywords: stochastic equations on graphs; fractional Brownian motion; parameter estimation stochastic equations on graphs; fractional Brownian motion; parameter estimation
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MDPI and ACS Style

Kříž, P.; Szała, L. The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise. Mathematics 2020, 8, 1766. https://doi.org/10.3390/math8101766

AMA Style

Kříž P, Szała L. The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise. Mathematics. 2020; 8(10):1766. https://doi.org/10.3390/math8101766

Chicago/Turabian Style

Kříž, Pavel, and Leszek Szała. 2020. "The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise" Mathematics 8, no. 10: 1766. https://doi.org/10.3390/math8101766

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