Constructions of local time for a Markov process

Bert Fristedt; S. J. Taylor

doi:10.1007/BF00532164

Constructions of local time for a Markov process

Bert Fristedt, S. J. Taylor

Mathematics

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10 Scopus citations

Abstract

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)
Pages (from-to)	73-112
Number of pages	40
Journal	Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume	62
Issue number	1
DOIs	https://doi.org/10.1007/BF00532164
State	Published - Mar 1 1983

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abstract = "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.",

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AB - 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.

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