Summary
LetX be a transient right process for which semipolar sets are polar. We characterize the measures which can arise as the distribution ofX T withT a non-randomized stopping time.
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[A73] Azéma, J.: Théorie générale des processus et retournement du temps. Ann. Sci. Éc. Norm. Super. (4)6, 459–519 (1973)
[BC74] Baxter, J.R., Chacon, R.V.: Potentials of stopped distributions. Ill. J. Math.18, 649–656 (1974)
[BG68] Blumenthal, R.M., Getoor, R.K.: Markov processes and potential theory. New York: Academic Press 1968
[B45] Brelot, M.: Minorantes sousharmoniques, extrémales, et capacités. J. Math. Pures Appl.24, 1–32 (1945)
[Ca80] Carmona, R.: Infinite dimensional Newtonian potentials. Probability theory on vector spaces II. (Lect. Notes Math. vol. 828, pp. 30–43) Berlin Heidelberg New York: Springer 1980
[Ch85] Chacon, P.R.M.: The filling scheme and barrier stopping times. Thesis, University of Washington, Seattle, 1985
[De69a] Dellacherie, C.: Ensembles aléatoires I. Sém. Prob. III. (Lect. Notes Math., vol. 88, pp. 97–114) Berlin Heidelberg New York: Springer 1969
[De69b] Dellacherie, C.: Ensembles aléatoires II. Sém. Prob. III. (Lect. Notes Math., vol. 88, pp. 115–136) Berlin Heidelberg New York: Springer 1969
[De88] Dellacherie, C.: Autour des ensembles semipolaires. Seminar on stochastic processes 1987, pp. 65–92. Boston: Birkhäuser 1988
[Du68] Dubins, L.E.: On a theorem of Skorokhod. Ann. Math. Stat.39, 2094–2097 (1968)
[Fa80] Falkner, N.: On Skorokhod embedding inn-dimensional Brownian motion by means of natural stopping times. Sém. Prob. XIV. (Lect. Notes Math., vol. 784, pp. 357–391) Berlin Heidelberg New York: Springer 1980
[Fa81] Falkner, N.: The distribution of Brownian motion in ℝ″ at a natural stopping time. Adv. Math.40, 97–127 (1981)
[Fa83] Falkner, N.: Stopped distributions for Markov processes in duality. Z. Wahrscheinlichkeitstheor. Verw. Geb.62, 43–51 (1983)
[Fe70] Fernique, X.: Intégrabilité des vecteurs gaussiens. C.R. Acad. Sci., Paris270, 1698–1699 (1970)
[Fi87] Fitzsimmons, P.J.: Homogeneous random measures and a weak order for the excessive measures of a Markov process. Trans. Am. Math. Soc.303, 431–478 (1987)
[Fi89] Fitzsimmons, P.J.: Markov processes and nonsymmetric Dirichlet forms without regularity. J. Funct. Anal.85, 287–306 (1989)
[Fi90] Fitzsimmons, P.J.: On the equivalence of three potential principles for right Markov processes. Probab. Th. Rel. Fields84, 251–265 (1990)
[Fi91] Fitzsimmons, P.J.: Skorokhod embedding by randomized hitting times. Seminar on stochastic processes 1990, pp. 183–191. Boston: Birkhäuser 1991
[FG88] Fitzsimmons, P.J., Getoor, R.K.: On the potential theory of symmetric Markov processes. Math. Ann.281, 495–512 (1988)
[FG90] Fitzsimmons, P.J., Getoor, R.K.: A fine domination principle for excessive measures. Math. Z. (in press)
[FM86] Fitzsimmons, P.J., Maisonneuve, B.: Excessive measures and Markov processes with random birth and death. Probab. Th. Rel. Fields72, 319–336 (1986)
[G80] Getoor, R.K.: Transience and recurrence of Markov processes. Sém. Prob. XIV. (Lect. Notes Math., vol. 784, pp. 397–409). Berlin Heidelberg New York: Springer 1980
[GG87] Getoor, R.K., Glover, J.: Constructing Markov processes with random times of birth and death. Seminar on stochastic processes 1986, pp. 35–69. Boston: Birkhäuser 1987
[GS84] Getoor, R.K., Sharpe, M.J.: Naturality, standardness, and weak duality for Markov processes. Z. Wahrscheinlichkeitstheor. Verw. Geb.67, 1–62 (1984)
[Ha79] Hawkes, J.: Potential theory of Lévy processes. Proc. Lond. Math. Soc. (3)38, 335–352 (1979)
[Hu57] Hunt, G.A.: Markoff processes and potentials I. Ill. J. Math.1, 44–93 (1957)
[Hu58] Hunt, G.A.: Markoff processes and potentials III. Ill. J. Math.2, 151–213 (1958)
[M82] Meyer, P.A.: Note sur les processus d'Ornstein-Uhlenbeck. Sém. Prob. XVI. (Lect. Notes Math., vol. 920, pp. 95–133) Berlin Heidelberg New York: Springer 1982
[Ro69] Root, D.H.: The existence of certain stopping times of Brownian motion. Ann. Math. Stat.40, 715–718 (1969)
[R70] Rost, H.: Die Stoppverteilungen eines Markoff-Prozesses mit lokalendlichem Potential. Manuscr. Math.3, 321–330 (1970)
[R71] Rost, H.: The stopping distributions of a Markov process. Invent. Math.14, 1–16 (1971)
[R73] Rost, H.: Skorokhod's theorem for general Markov processes. Proc. Sixth Prague Conf. on Information Theory. Prague: Prague Publishing House of the Czechoslovak Academy of Sciences 1973
[R76] Rost, H.: Skorokhod stopping times of minimal variance. Sém. Prob. X. (Lect. Notes Math., vol. 511, pp. 194–208) Berlin Heidelberg New York: Springer 1976
[Sh88] Sharpe, M.J.: General theory of Markov processes. New York: Academic Press 1988
[Si77] Silverstein, M.L.: The sector condition implies that semipolar sets are quasi-polar. Z. Wahrscheinlichkeitstheor. Verw. Geb.41, 13–33 (1977)
[Sk60] Skorokhod, A.V.: A limit theorem for sums of independent random variables [Russian]. Dokl. Akad. Nauk. SSSR133, 34–35 (1960)
[Sk65] Skorokhod, A.V.: Studies in the theory of random processes. Reading, Mass: Addison-Wesley 1965
[SW73] Smythe, R.T., Walsh, J.B.: The existence of dual processes. Invent. Math.19, 113–148 (1973)
[V70] Varadarajan, V.S.: Geometry of quantum theory, vol. 2. New York: Van Nostrand Reinhold 1970
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This work was done while the first-named author was visiting the University of California, San Diego
The second-named author's research is supported in part by NSF grant DMS8721347
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Falkner, N., Fitzsimmons, P.J. Stopping distributions for right processes. Probab. Th. Rel. Fields 89, 301–318 (1991). https://doi.org/10.1007/BF01198789
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DOI: https://doi.org/10.1007/BF01198789