×

Path continuity and last exit distributions. (English) Zbl 0537.60081

Sémin. probabilités XVIII, 1982/83, Proc., Lect. Notes Math. 1059, 119-126 (1984).
[For the entire collection see Zbl 0527.00020.]
The path continuity of a Markov process implies that both its hitting distributions and its last exit distributions are concentrated on the boundaries. While the hitting distributions being concentrated on the boundaries also implies the path continuity, it is not so for last exit distributions. In this paper, we first present an example of a discontinuous Hunt process whose last exit distributions are concentrated on the boundaries, then we show that, under an additional condition, the last exit distributions being concentrated on the boundaries is equivalent to the path continuity. In particular, the above equivalence holds if the hitting probability of a compact set is continuous on its complement and the hitting probability of a point is less than one.

MSC:

60J40 Right processes
60G17 Sample path properties

Citations:

Zbl 0527.00020
Full Text: Numdam EuDML