The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise

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) an...

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Bibliographic Details
Published in:Mathematics
Main Authors: Pavel Kříž, Leszek Szała
Format: Article
Language:English
Published: MDPI AG 2020-10-01
Subjects:
stochastic equations on graphs
fractional Brownian motion
parameter estimation
Online Access:https://www.mdpi.com/2227-7390/8/10/1766
Description
Summary: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.
ISSN:2227-7390

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