Sequential Inference for Non-Gaussian Additive Processes

Zixin Liu

doi:10.1109/OJSP.2025.3648708

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Sequential Inference for Non-Gaussian Additive Processes

2025-12-25

Zixin Liu

Simon Godsill

DOI：10.1109/OJSP.2025.3648708

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Abstract

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In this paper, we introduce dynamical models based on Stochastic Differential Equations (SDE)s driven by additive processes. Additive processes are intuitively obtained as time-varying versions of Lévy processes, and we adopt this formalism to model properties that may change over time, for example the skewness of the process. While the framework is quite general, we take an $\alpha$-stable process with time-varying skew as a concrete example, demonstrating the effect of time-varying skew on the expected direction of motion of an object. The framework is constructed based on a generalised shot-noise representation of an additive process. We show how to perform joint inference about states and skew of the model, based on a marginalised particle filter framework. Finally, performance is demonstrated on both simulated and real data and improved performance is observed compared with competitor models.

Keywords:

Non-Gaussian stochastic process

sequential Monte Carlo

particle filter

Lévy process

additive process

stochastic differential equation

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