A continuous time Markov chain is observed with Gaussian white noise
added to it. To the well-known problem of continuously estimating the current
state of the chain, we introduce the additional option of continuously varying
the sampling rates, as long as some restriction (or cost) on the average
sampling rate is satisfied. The optimal solution to this "dynamic sampling"
problem is presented and analyzed in closed form for the two-state symmetric
case. It is shown that the resulting dynamic sampling procedure has a much
lower asymptotic average error rate compared to the one obtained when sampling
at a constant rate. Alternatively, the dynamic sampling procedure can provide
the same error rate using a much lower average sampling rate. The relative
efficiency of the dynamic sampling procedure may in fact tend to infinity in
some extreme cases.
Publié le : 1997-08-14
Classification:
Filtering,
dynamic sampling,
Gaussian white noise,
diffusion process,
optimal control,
average error rate,
62M20,
93E20,
60J27,
60J60
@article{1034801256,
author = {Assaf, David},
title = {Estimating the state of a noisy continuous time Markov chain when
dynamic sampling is feasible},
journal = {Ann. Appl. Probab.},
volume = {7},
number = {1},
year = {1997},
pages = { 822-836},
language = {en},
url = {http://dml.mathdoc.fr/item/1034801256}
}
Assaf, David. Estimating the state of a noisy continuous time Markov chain when
dynamic sampling is feasible. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp. 822-836. http://gdmltest.u-ga.fr/item/1034801256/