Markov Process Jump Times and Their Cox Construction
Probability
2023-10-12 v1
Abstract
In this short paper, we connect the procedure of constructing a totally inaccessible stopping time for a given process using the well-known Cox construction, dependent on an independent exponential random variable; with naturally occurring jump times of Feller processes. Ultimately, we show that these two phenomena are not only related, but are in fact two examples of the same object. We link this fact to the behaviour of predictable stopping times, by proving that they can always be written as the hitting time of zero of a continuous process.
Keywords
Cite
@article{arxiv.2310.07003,
title = {Markov Process Jump Times and Their Cox Construction},
author = {Philip Protter and Andrés Riveros Valdevenito},
journal= {arXiv preprint arXiv:2310.07003},
year = {2023}
}
Comments
11 pages