Abstract
In the following we will let (X, U) and (Y, V) denote P-harmonic spaces in the sense of Constantinescu and Cornea [3]. (X, Y are locally compact Hausdorff spaces with countable bases and U, V are hyperharmonic sheaves on respectively.) We will assume that the constant function 1 is hyperharmonic. It is now well known that there exist Hunt processes Xt,Yt on X, V with continuous paths (i.e. diffusions) such that the family of Xt-excessive, resp. Yt-excessive, functions coincide with the family of non-negative U-hyperharmonic, resp. V-hyperharmonic, functions.
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References
Blumenthal, R.M., Getoor, R.K., and McKean, H.P., Markov processes with identical hitting distributions, Illinois J. Math., 6 (1962), 402–420 and 7 (1963), 540–542.
Bliedtner, J., and Hansen, W., 1986, “Potential Theory”, Springer-Verlag.
Constantinescu, C., and Cornea, A., 1972, “Potential Theory on Harmonic Spaces”, Springer-Verlag.
Csink, L., and Øksendal, B., A stochastic characterization of harmonic morphisms. (To appear).
Getoor, R.K., 1975, “Markov Processes: Ray Processes and Right Processes”, Springer LNM 440.
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© 1988 Plenum Press, New York
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Csink, L., Øksendal, B. (1988). Harmonic Morphisms and Ray Processes. In: Král, J., Lukeš, J., Netuka, I., Veselý, J. (eds) Potential Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0981-9_10
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DOI: https://doi.org/10.1007/978-1-4613-0981-9_10
Publisher Name: Springer, Boston, MA
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