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Harmonic Morphisms and Ray Processes

In: Potential Theory

Author

Listed:
  • Laszlo Csink

    (Eötvös University)

  • Bernt Øksendal

    (University of Oslo, Department of Mathematics)

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.

Suggested Citation

  • Laszlo Csink & Bernt Øksendal, 1988. "Harmonic Morphisms and Ray Processes," Springer Books, in: Josef Král & Jaroslav Lukeš & Ivan Netuka & Jiří Veselý (ed.), Potential Theory, pages 71-74, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0981-9_10
    DOI: 10.1007/978-1-4613-0981-9_10
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