Summary
Suppose X t is a purely discontinuous martingale. A sufficient condition for X t to have a local time is given in terms of the local characteristics of X. An example is constructed to show that this condition is nearly optimal.
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Bass, R.F. Local times for a class of purely discontinuous martingales. Z. Wahrscheinlichkeitstheorie verw Gebiete 67, 433–459 (1984). https://doi.org/10.1007/BF00532048
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DOI: https://doi.org/10.1007/BF00532048