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Bridges of Markov counting processes: quantitative estimates. (English) Zbl 1338.60195

Summary: 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 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.

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
60J75 Jump processes (MSC2010)
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