The problem of finding minimax sequential estimation procedures for stochastic processes is considered. It is assumed that in addition to the loss associated with the error of estimation a cost of observing the process is incurred. A class of minimax sequential procedures is derived explicitly for a one-parameter exponential family of stochastic processes. The minimax sequential procedures are presented in some special models, in particular, for estimating a parameter of exponential families of diffusions, for estimating the mean or drift coefficients of the class of Ornstein-Uhlenbeck processes, for estimating the drift of a geometric Brownian motion and for estimating a parameter of a family of counting processes. A class of minimax sequential rules for a compound Poisson process with multinomial jumps is also found.
@article{bwmeta1.element.bwnjournal-article-zmv25i1p1bwm,
author = {Ryszard Magiera},
title = {On minimax sequential procedures for exponential families of stochastic processes},
journal = {Applicationes Mathematicae},
volume = {25},
year = {1998},
pages = {1-18},
zbl = {0895.62084},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv25i1p1bwm}
}
Magiera, Ryszard. On minimax sequential procedures for exponential families of stochastic processes. Applicationes Mathematicae, Tome 25 (1998) pp. 1-18. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv25i1p1bwm/
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