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.*
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(Submitted)

Full text not available from this repository.

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 |
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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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