Completely asymmetric stable processes conditioned to avoid an interval
Probability
2020-02-19 v1
Abstract
In the recent article D\"oring et al. [4] the authors conditioned a stable process with two-sided jumps to avoid an interval. As usual the strategy was to find an invariant function for the process killed on entering the interval and to show that the corresponding h-transformed process is indeed the process conditioned to avoid an interval in a meaningful way. In the present article we consider the case of a completely asymmetric stable process. It turns out that the invariant function found in [4] does not exist or is not invariant but nonetheless, we will characterize the conditioned process as a Markov process.
Cite
@article{arxiv.1906.06928,
title = {Completely asymmetric stable processes conditioned to avoid an interval},
author = {Pierre Lenthe and Philip Weissmann},
journal= {arXiv preprint arXiv:1906.06928},
year = {2020}
}
Comments
10 pages. arXiv admin note: text overlap with arXiv:1807.08466