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References
Blumenthal, R.M., Getoor, R.K.: Markov processes and potential theory. New York and London: Academic Press 1968.
— —, McKean, H.P., Jr.: Markov processes with identical hitting distributions. Illinois J. Math. 6, 402–420 (1962).
Boboc, N., Constantinescu, C., Cornea, A.: Semigroups of transitions on harmonic spaces. Revue Roumaine Math. pur. appl. 12, 763–805 (1967).
Bochner, S.: Harmonic analysis and the theory of probability. Berkeley, California: University of California Press (1955).
Dawson, D.A.: The construction of a class of diffusions. Illinois J. Math. 8, 657–684 (1964).
Hansen, W.: Konstruktion von Halbgruppen und Markoffschen Prozessen. Inventiones math. 3, 179–214 (1967).
—: Charakterisierung von Familien exzessiver Funktionen. Inventiones math. 5, 335–348 (1968).
Hunt, G.A.: Markoff processes and potentials, I, II and IV. Illinois J. Math, 1, 44–93, 316–369 (1957); and 2, 151–213 (1958).
Knight, F., Orey, S.: Construction of a Markov process from hitting probabilities. J. Math. Mech. 13, 857–873 (1964).
Meyer, P.A.: Brelot's axiomatic theory of the Dirichlet problem and Hunt's theory. Ann. Inst. Fourier 13/2, 357–372 (1963).
Shih, C.T.: Construction of Markov processes from hitting probabilities, abstract. Notices Amer. math. Soc. 13, 234 (1966).
—: Markov processes whose hitting distributions are dominated by those of a given process. Trans. Amer. math. Soc. 129, 157–179 (1967).
Skorokhod, A.V.: Limit theorems for Markov processes. Theor. Probab. Appl. 3, 202–245 (1958).
Stone, C.: Weak convergence of stochastic processes defined on semi-infinite time intervals. Proc. Amer. math. Soc. 14, 694–696 (1963).
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This research was supported by an ONR Research Associateship at Cornell University and by NSF Grant GP-6549.
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Shih, C.T. Construction of markov processes from hitting distributions. Z. Wahrscheinlichkeitstheorie verw Gebiete 18, 47–72 (1971). https://doi.org/10.1007/BF00538487
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DOI: https://doi.org/10.1007/BF00538487