# Deep Learning for the Benes Filter

@article{Lobbe2022DeepLF, title={Deep Learning for the Benes Filter}, author={Alexander Lobbe}, journal={ArXiv}, year={2022}, volume={abs/2203.05561} }

The Benes filter is a well-known continuous-time stochastic filtering model in one dimension that has the advantage of being explicitly solvable. From an evolution equation point of view, the Benes filter is also the solution of the filtering equations given a particular set of coefficient functions. In general, the filtering stochastic partial differential equations (SPDE) arise as the evolution equations for the conditional distribution of an underlying signal given partial, and possibly…

## 2 Citations

### An energy-based deep splitting method for the nonlinear filtering problem

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A deep splitting method is combined with an energy-based model for the approximation of functions by a deep neural network to result in a computationally fast nonlinear learner that takes observations as input and that does not require re-training when new observations are received.

### Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis

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