Filtering for some stochastic processes with discrete observations.

摘要

The processes in question are jump processes and processes with jumping velocity. We estimate the current position of the stochastic process based on past discrete-time observations (non-linear discrete filtering problem). We obtain asymptotic rates for the expected square error of the filter when observations become frequent. These rates are better than those of a linear Kalman filter. For jump process, our method is asymptotically free of the process parameters. Also, estimation of process parameters is addressed.