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Local time for processes indexed by a partially ordered set

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  • Ivanoff, B. Gail
  • Sawyer, P.

Abstract

Local time with respect to an arbitrary random measure is defined for a process indexed by a partially ordered set (poset). When the parameter space is a product of posets and local times exist for the projections of the process in one direction, then under very general conditions it is shown that local time exists for the original process. This general theorem is shown to include many known results for multidimensional martingales and as well can be applied to martingales indexed by sets.

Suggested Citation

  • Ivanoff, B. Gail & Sawyer, P., 2003. "Local time for processes indexed by a partially ordered set," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 1-15, January.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:1:p:1-15
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    References listed on IDEAS

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    1. Imkeller, Peter, 1986. "Local times of continuous N-parameter strong martingales," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 348-365, August.
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    Cited by:

    1. Cassese, Gianluca, 2010. "Supermartingale decomposition with a general index set," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1060-1073, July.

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