Constructions of local time for a Markov process

  • Bert Fristedt
  • S. J. Taylor
Article

DOI: 10.1007/BF00532164

Cite this article as:
Fristedt, B. & Taylor, S.J. Z. Wahrscheinlichkeitstheorie verw Gebiete (1983) 62: 73. doi:10.1007/BF00532164

Summary

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.

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Bert Fristedt
    • 1
  • S. J. Taylor
    • 2
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of Pure MathematicsLiverpool UniversityLiverpoolEngland