Prediction from a Random Time Point
Lindgren, Georg
Ann. Probab., Tome 3 (1975) no. 6, p. 412-423 / Harvested from Project Euclid
In prediction (Wiener-, Kalman-) of a random normal process $\{X(t), t \in R\}$ it is normally required that the time $t_0$ from which prediction is made does not depend on the values of the process. If prediction is made only from time points at which the process takes a certain value $u,$ given a priori, ("prediction under panic"), the Wiener-prediction is not necessarily optimal; optimal should then mean best in the long run, for each single realization. The main theorem in this paper shows that when predicting only from upcrossing zeros $t_\nu$, the Wiener-prediction gives optimal prediction of $X(t_\nu + t)$ as $t_\nu$ runs through the set of zero upcrossings, if and only if the derivative $X'(t_\nu)$ at the crossing points is observed. The paper also gives the conditional distribution from which the optimal predictor can be computed.
Publié le : 1975-06-14
Classification:  Prediction,  zero-crossings,  stopping times,  60G25,  62M20,  60G40
@article{1176996349,
     author = {Lindgren, Georg},
     title = {Prediction from a Random Time Point},
     journal = {Ann. Probab.},
     volume = {3},
     number = {6},
     year = {1975},
     pages = { 412-423},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996349}
}
Lindgren, Georg. Prediction from a Random Time Point. Ann. Probab., Tome 3 (1975) no. 6, pp.  412-423. http://gdmltest.u-ga.fr/item/1176996349/