Let $X(t)$ be a measurable stochastic process on a countably generated space $(E, \mathscr{E})$, and let $G(t) = \cap_{\delta>o} \mathscr{F}^\circ (t, t + \delta)$ be its germ field. By transferring the probabilities to a representation space, we define and analyze the class of such processes which are Markovian relative to $G(t)$ and autonomous, in the sense that they have a stationary transition mechanism. These processes are reduced to Ray processes on an abstract space with a certain weak topology. Five kinds of examples are indicated.
Publié le : 1979-06-14
Classification:
Germ-Markov property,
right process,
Ray process,
prediction,
transition function,
60J25,
60J35,
60G05
@article{1176995041,
author = {Knight, Frank B.},
title = {Prediction Processes and an Autonomous Germ-Markov Property},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 385-405},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995041}
}
Knight, Frank B. Prediction Processes and an Autonomous Germ-Markov Property. Ann. Probab., Tome 7 (1979) no. 6, pp. 385-405. http://gdmltest.u-ga.fr/item/1176995041/