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.
|Original language||English (US)|
|Number of pages||40|
|Journal||Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete|
|State||Published - Mar 1983|