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June, 1979 Prediction Processes and an Autonomous Germ-Markov Property
Frank B. Knight
Ann. Probab. 7(3): 385-405 (June, 1979). DOI: 10.1214/aop/1176995041

Abstract

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.

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Frank B. Knight. "Prediction Processes and an Autonomous Germ-Markov Property." Ann. Probab. 7 (3) 385 - 405, June, 1979. https://doi.org/10.1214/aop/1176995041

Information

Published: June, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0399.60066
MathSciNet: MR528318
Digital Object Identifier: 10.1214/aop/1176995041

Subjects:
Primary: 60J25
Secondary: 60G05, 60J35

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 3 • June, 1979
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