Constructions of local time for a Markov process
- Cite this article as:
- Fristedt, B. & Taylor, S.J. Z. Wahrscheinlichkeitstheorie verw Gebiete (1983) 62: 73. doi:10.1007/BF00532164
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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.