Bridges of Markov counting processes: quantitative estimates
Probability
2015-12-04 v1
Abstract
In this paper we investigate the behavior of the bridges of a Markov counting process in several directions. We first characterize convexity(concavity) in time of the mean value in terms of lower (upper) bounds on the so called \textit{reciprocal characteristics}. This result gives a natural criterion to determine whether bridges are "lazy" or "hurried". Under the hypothesis of global bounds on the reciprocal characteristics we prove sharp estimates for the marginal distributions and a comparison theorem for the jump times. When the height of the bridge tends to infinity we show the convergence to a deterministic curve, after a proper rescaling.
Keywords
Cite
@article{arxiv.1512.01180,
title = {Bridges of Markov counting processes: quantitative estimates},
author = {Giovanni Conforti},
journal= {arXiv preprint arXiv:1512.01180},
year = {2015}
}