Repository: Freie Universit├Ąt Berlin, Math Department

Statistical learning of non-linear stochastic differential equations from non-stationary time-series using variational clustering

Boyko, V. and Krumscheid, S. and Vercauteren, N. (2021) Statistical learning of non-linear stochastic differential equations from non-stationary time-series using variational clustering. . . (Submitted)

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Official URL: https://arxiv.org/abs/2102.12395

Abstract

Parameter estimation for non-stationary stochastic differential equations (SDE) with an arbitrary non-linear drift and non-linear diffusion is accomplished in combination with a non-parametric clustering methodology. Such a model-based clustering approach includes a quadratic programming (QP) problem with equality and inequality constraints. We couple the QP problem to a closed-form likelihood function approach based on suitable Hermite-expansions to approximate the parameter values of the SDE model. The classification problem provides a smooth indicator function, which enables us to recover the underlying temporal parameter modulation of the one-dimensional SDE. As shown by the numerical examples, the clustering approach recovers a hidden functional relationship between the SDE model parameters and an additional auxiliary process. The study builds upon this functional relationship to develop closed-form, non-stationary, data-driven stochastic models for multiscale dynamical systems in real-world applications.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2506
Deposited By: Ulrike Eickers
Deposited On:04 Mar 2021 14:42
Last Modified:04 Mar 2021 16:29

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