Following Choquet, the capacity associated with a Markov process is said to be dichotomous if each compact set $K$ contains two disjoint sets with the same capacity as $K$. In the context of right processes, we prove that the dichotomy of capacity is equivalent to Hunt's hypothesis that semipolar sets are polar. We also show that a weaker form of the dichotomy is valid for any Levy process with absolutely continuous potential kernel.
Publié le : 1992-01-14
Classification:
Capacity,
dichotomy,
semipolar,
right process,
60J45,
60J25
@article{1176989930,
author = {Fitzsimmons, P. J. and Kanda, Mamoru},
title = {On Choquet's Dichotomy of Capacity for Markov Processes},
journal = {Ann. Probab.},
volume = {20},
number = {4},
year = {1992},
pages = { 342-349},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989930}
}
Fitzsimmons, P. J.; Kanda, Mamoru. On Choquet's Dichotomy of Capacity for Markov Processes. Ann. Probab., Tome 20 (1992) no. 4, pp. 342-349. http://gdmltest.u-ga.fr/item/1176989930/