The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise

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.