no. 3-4
The Ray space of a right process
Annales de l'Institut Fourier, Volume 25 (1975) no. 3-4, pp. 207-233

Let X be a process with state space E satisfying (a somewhat relaxed version of) Meyer’s “hypothèses droites”. Then by introducing a new topology (called the Ray topology) on E and a compactification F of E in the Ray topology one can regard X as a Ray process. However, this construction depends on the choice of an arbitrary uniformity on E and not just the topology of E. We show that the Ray topology is independent of the choice of this uniformity. We then introduce a space R (the Ray space) which contains E in the Ray topology and which has all of the properties of F which are relevant for the study of X. Although R is not compact it is independent of the choice of the original uniformity on E.

Soit X un processus de Markov à valeurs dans un espace d’états E, satisfaisant à des hypothèses un peu plus faibles que les hypothèses droites de Meyer. Après avoir introduit une topologie nouvelle sur E, que l’on appelle topologie de Ray, et un compactifié F de E pour cette topologie, on peut identifier X à un processus de Ray. Cependant, cette construction dépend du choix d’une uniformité sur E, et non seulement de la topologie de E. Nous montrons que la topologie de Ray ne dépend pas de l’uniformité choisie. On introduit un espace R, l’espace de Ray, qui contient E dans sa topologie de Ray, et qui possède toutes les propriétés de F que l’on veut pour l’étude de X. Bien que R ne soit pas compact, il est indépendant de l’uniformité.

@article{AIF_1975__25_3-4_207_0,
     author = {Getoor, Ronald K. and Sharpe, Michael J.},
     title = {The {Ray} space of a right process},
     journal = {Annales de l'Institut Fourier},
     pages = {207--233},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {25},
     number = {3-4},
     year = {1975},
     doi = {10.5802/aif.580},
     mrnumber = {53 #9396},
     zbl = {0304.60005},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.580/}
}
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Getoor, Ronald K.; Sharpe, Michael J. The Ray space of a right process. Annales de l'Institut Fourier, Volume 25 (1975) no. 3-4, pp. 207-233. doi: 10.5802/aif.580

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