Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

, Volume 62, Issue 1, pp 73-112

Constructions of local time for a Markov process

  • Bert FristedtAffiliated withSchool of Mathematics, University of Minnesota
  • , S. J. TaylorAffiliated withDepartment of Pure Mathematics, Liverpool University

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A sequence of functions defined on the space of excursions of a Markov process from a fixed point is considered. For each of the functions the sum over the excursions that begin by time t is normalized in an appropriate manner. Conditions are obtained for the convergence of the sequence of normalized sums to the local time evaluated at time t. We obtain a unified structure for convergence theorems which includes some new constructions of local time as well as many constructions previously obtained by quite varied techniques.