On the stochastic behavior of optional processes up to random times

Details On the stochastic behavior of optional processes up to random times On the stochastic behavior of optional processes up to random times

2010-07-07

arxiv.org/abs/1007.1124v3

Mathematics

Probability

33 pages. Second, thoroughly revised version. Theoretical results have been removed and more examples are given

Scientific paper

In this paper, a study of random times on filtered probability spaces is undertaken. The main message is that, as long as distributional properties of optional processes up to the random time are involved, there is no loss of generality in assuming that the random time is actually a randomized stopping time. This perspective has advantages in both the theoretical and practical study of optional processes up to random times. Applications are given to the stochastic behavior of processes up to times of overall maximum and last-passage times in the context of downwards drifting Levy processes with no positive jumps, as well as downwards transient diffusions.

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