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2016 Bridges of Markov counting processes: quantitative estimates
Giovanni Conforti
Electron. Commun. Probab. 21: 1-13 (2016). DOI: 10.1214/16-ECP4762

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 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.

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Giovanni Conforti. "Bridges of Markov counting processes: quantitative estimates." Electron. Commun. Probab. 21 1 - 13, 2016. https://doi.org/10.1214/16-ECP4762

Information

Received: 14 December 2015; Accepted: 16 February 2016; Published: 2016
First available in Project Euclid: 26 February 2016

zbMATH: 1338.60195
MathSciNet: MR3485388
Digital Object Identifier: 10.1214/16-ECP4762

Subjects:
Primary: 60J27 , 60J75

Keywords: Bridges , counting processes , duality formula , tail estimates

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