# The Ray space of a right process

Ronald K. Getoor; Michael J. Sharpe

Annales de l'institut Fourier (1975)

- Volume: 25, Issue: 3-4, page 207-233
- ISSN: 0373-0956

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topGetoor, Ronald K., and Sharpe, Michael J.. "The Ray space of a right process." Annales de l'institut Fourier 25.3-4 (1975): 207-233. <http://eudml.org/doc/74243>.

@article{Getoor1975,

abstract = {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 $E$.},

author = {Getoor, Ronald K., Sharpe, Michael J.},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {3-4},

pages = {207-233},

publisher = {Association des Annales de l'Institut Fourier},

title = {The Ray space of a right process},

url = {http://eudml.org/doc/74243},

volume = {25},

year = {1975},

}

TY - JOUR

AU - Getoor, Ronald K.

AU - Sharpe, Michael J.

TI - The Ray space of a right process

JO - Annales de l'institut Fourier

PY - 1975

PB - Association des Annales de l'Institut Fourier

VL - 25

IS - 3-4

SP - 207

EP - 233

AB - 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 $E$.

LA - eng

UR - http://eudml.org/doc/74243

ER -

## References

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- [3] R. K. GETOOR, Lectures on Markov Processes : Ray Processes and Right Processes, Preliminary Version Univ. of Calif. San Diego (1974). To appear Springer Lecture Notes in Mathematics.
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- [5] P. A. MEYER, Probability and Potentials, Ginn. Boston (1966). Zbl0138.10401MR34 #5119
- [6] P. A. MEYER and J. B. WALSH, Quelques applications des résolvantes de Ray, Invent. Math., 14 (1971), 143-166. Zbl0224.60037MR45 #4502
- [7] M. OHTSUKA, Dirichlet Problem, Extremal Length, and Prime Ends, Van Nostrand Reinhold Math. Studies, 22 (1970). Zbl0197.08404
- [8] K. P. PARTHASARATHY, Probability Measures on Metric Spaces, Academic Press, New York (1967). Zbl0153.19101MR37 #2271
- [9] D. B. RAY, Resolvents, transition functions, and strongly Markovian processes, Ann. Math., 70 (1959), 43-72. Zbl0092.34501
- [10] C. T. SHIH, On extending potential theory to all strong Markov processes, Ann. Instit. Fourier, 20 (1970), 303-315. Zbl0193.46201MR44 #6040

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