Pavel Chigansky (Weizmann Institute)
The first part of this talk is intended as an introduction to the filtering problem for
random processes, i.e., the optimal estimation of signals from the past of the their noisy
observations. The standard setting here consists of a pair of processes (X,Y)=(X_t,Y_t).
where the signal component X is to be estimated at a current time t>0 on the basis of the
trajectory of Y , observed up to this t . Under the minimal mean square error (MMSE)
criterion, the optimal estimate of X_t is the conditional expectation of X given the
process Y up to time t. If both X and (X,Y) are Markov processes, then the conditional
distribution satisfies a recursive equation, called filter, which realizes the optimal fusion
of the a priori statistical knowledge about the signal and the a posteriori information
borne by the observation path.
In the second part, I will touch upon the recent progress in stability problem for