On the anticipative nonlinear filtering problem and its stability

Guang Lin; Yanghui Liu; Samy Tindel

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arXiv · 1902.08168

On the anticipative nonlinear filtering problem and its stability

Guang Lin·Yanghui Liu·Samy Tindel

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Abstract

In this paper, we consider an anticipative nonlinear filtering problem, in which the observation noise is correlated with the past of the signal. This new signal-observation model has its applications in both finance models with insider trading and in engineering. We derive a new equation for the filter in this context, analyzing both the nonlinear and the linear cases. We also handle the case of a finite filter with Volterra type observation. The performance of our algorithm is presented through numerical experiments.

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Guang Lin, Yanghui Liu, Samy Tindel. 2019-02-21. On the anticipative nonlinear filtering problem and its stability. https://arxiv.org/abs/1902.08168

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