# Generalised Hyperbolic State-space Models for Inference in Dynamic Systems

arXiv: https://arxiv.org/abs/2309.11422 · HTML: https://mlsanity.com/paper/2309.11422/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Sep 2023.

## Built on by (most cited first, 2 of 2)

- [Integrated Gaussian Processes for Robust and Adaptive Multi-Object Tracking](https://mlsanity.com/paper/2507.04116/) (2025)
- [Variational Inference for L'evy Process-Driven SDEs via Neural Tilting](https://mlsanity.com/paper/2605.10934/) (2026)

## Abstract (arXiv)

In this work we study linear vector stochastic differential equation (SDE) models driven by the generalised hyperbolic (GH) L'evy process for inference in continuous-time non-Gaussian filtering problems. The GH family of stochastic processes offers a flexible framework for modelling of non-Gaussian, heavy-tailed characteristics and includes the normal inverse-Gaussian, variance-gamma and Student-t processes as special cases. We present continuous-time simulation methods for the solution of vector SDE models driven by GH processes and novel inference methodologies using a variant of sequential Markov chain Monte Carlo (MCMC). As an example a particular formulation of Langevin dynamics is studied within this framework. The model is applied to both a synthetically generated data set and a real-world financial series to demonstrate its capabilities.