Stability of the optimal filter w.r.t. its initial condition
speaker: Wilhelm Stannat (Fakultaet fuer Matematik, Universitaet Bielefeld, Germany)abstract: Estimating a Markovian signal process observed with independent noise has many important applications not only in engineering sciences. The optimal estimate of the signal depends, of course, on the one hand on the observations but on the other hand also on the initial state of the signal. Since the signal is not observed directly, its initial state, however, is unknown. It is therefore important to understand the dependence of the optimal filter w.r.t. the initial state. In our talk we show how a variational approach can be used to understand this dependence and how to obtain explicit a priori lower bounds on the rate of stability. Our results are helpful for the design of efficient measurements. The main tool in our analysis will be a description of the filter with the help of a stochastic partial differential equation. Ergodicity of the signal process is not needed. We will also have a closer look at a particular class of signal processes with multiplicative noise arising in the theory of software reliability.
timetable:
Wed 5 Apr, 11:50 - 12:30, Aula Dini
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