English

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}
}
R2 v1 2026-06-22T12:00:52.137Z