Level numbers preserving transformations on excursionsdefined by random walks with state dependent jump laws
Probability
2023-07-27 v1
Abstract
We study the number of individuals per level defined by excursions of random walks with state dependent jump law. These level numbersdetermine the probability of the excursion, and the set of transformations preserving the level numbers is, generically, the set of transformation that preserve the probability law of excursions.We compute the number of excursions having a fixed level numbers and we show that the class of shifts of excursions generate all the excursions having a fixed level numbers. We study the behaviorof the level numbers under the Vervaat transform and the Doob transform.
Cite
@article{arxiv.2307.14002,
title = {Level numbers preserving transformations on excursionsdefined by random walks with state dependent jump laws},
author = {Thierry Huillet and Servet Martinez},
journal= {arXiv preprint arXiv:2307.14002},
year = {2023}
}