The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise

Pavel Kříž and Leszek Szała
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Pavel Kříž: Department of Mathematics, Faculty of Chemical Engineering, University of Chemistry and Technology Prague, 16628 Prague, Czech Republic
Leszek Szała: Department of Mathematics, Faculty of Chemical Engineering, University of Chemistry and Technology Prague, 16628 Prague, Czech Republic

Mathematics, 2020, vol. 8, issue 10, 1-21

Abstract: 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.

Keywords: stochastic equations on graphs; fractional Brownian motion; parameter estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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