We show three different robustness resultswith respect to the
modelling of the system process for the optimal filter in the
classical nonlinear filtering problem. More precisely it is shown
that if the system process is given by a markovian SDE, then under
rather strict assumptions, the optimal filter is L_p-continuous
with respectto the sup-norm on thecoefficients in the system
process. Then it is shown that if the system process is given by a
nonmarkovian SDEthe filter is pathwise continuous with respect to
the drift term for fixed diffusion term bounded away from 0.
Lastly it is proven that for general RCLL system processes, there
iscontinuity with respect to the weak topology on probability
measures in the sense that if a sequence of RCLL processes
converges in distribution to the system process, a sequence of
probability measures corresponding to theerroneous filters
converges weakly towards a probability measure associated with the
correct filter.

Number of pages | 25 |
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Publication status | Published - 1996 |
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