| Abstract: |
| I will discuss the filtering of partially observed diffusions, with discrete-time observations. It is assumed that only biased approximations of the diffusion can be obtained, for choice of an accuracy parameter. A multilevel estimator is proposed, consisting of a telescopic sum of increment estimators associated to the successive levels. The work associated to a given mean-square error between the multilevel estimator and average with respect to the filtering distribution is shown to scale optimally, for optimal rates of convergence of the underlying diffusion approximation. The method is illustrated on some examples. |
|