Stability of the optimal filter in continuous time: Beyond the bene{\v s} filter
Probability
2020-01-29 v3 Optimization and Control
Statistics Theory
Statistics Theory
Abstract
We are interested in the optimal filter in a continuous time setting. We want to show that the optimal filter is stable with respect to its initial condition. We reduce the problem to a discrete time setting and apply truncation techniques coming from [OR05]. Due to the continuous time setting, we need a new technique to solve the problem. In the end, we show that the forgetting rate is at least a power of the time t. The results can be re-used to prove the stability in time of a numerical approximation of the optimal filter.
Keywords
Cite
@article{arxiv.1604.03345,
title = {Stability of the optimal filter in continuous time: Beyond the bene{\v s} filter},
author = {van Bien Bui and Sylvain Rubenthaler},
journal= {arXiv preprint arXiv:1604.03345},
year = {2020}
}