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We are interested in the optimal filter in a continuous time setting. We wantto show that the optimal filter is stable with respect to its initialcondition. We reduce the problem to a discrete time setting and applytruncation 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 theforgetting rate is at least a power of the time t. The results can be re-usedto prove the stability in time of a numerical approximation of the optimalfilter.

Stability of the optimal filter in continuous time: Beyond the bene{\v s} filter