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Lookup NU author(s): Dr Quentin Clairon
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
Multi-dimensional stochastic differential equations (SDEs) are a powerful tool to describe dynamics of phenomena that change over time. We focus on the parametric estimation of such SDEs based on partial observations when only a one-dimensional component of the system is observable. We consider two families of SDE, the elliptic family with a full-rank diffusion coefficient and the hypoelliptic family with a degenerate diffusion coefficient. Estimation for the second class is much more difficult and only few estimation methods have been proposed. Here, we adopt the framework of the optimal control theory to derive a contrast (or cost function) based on the best control sequence mimicking the (unobserved) Brownian motion. We propose a full data-driven approach to estimate the drift and diffusion coefficient parameters. Numerical simulations made on different examples (Harmonic Oscillator, FitzHugh–Nagumo, Lotka–Volterra) reveal our method produces good pointwise estimate for an acceptable computational price with, interestingly, no performance drop for hypoelliptic systems.
Author(s): Clairon Q, Samson A
Publication type: Article
Publication status: Published
Journal: Statistical Inference for Stochastic Processes
Online publication date: 25/06/2019
Acceptance date: 11/06/2019
Date deposited: 28/06/2019
ISSN (print): 1387-0874
ISSN (electronic): 1572-9311
Publisher: Springer Netherlands
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