# Poissons ensemble of loops of one-dimensional diffusions

@article{Lupu2013PoissonsEO,
title={Poissons ensemble of loops of one-dimensional diffusions},
author={Titus Lupu},
journal={arXiv: Probability},
year={2013},
volume={157},
pages={1-162}
}
• Titus Lupu
• Published 15 February 2013
• Mathematics
• arXiv: Probability
We study the analogue of Poisson ensembles of Markov loops ('loop soups') in the setting of one-dimensional diffusions. We give a detailed description of the corresponding intensity measure. The properties of this measure on loops lead us to an extension of Vervaat's bridge-to-excursion transformation that relates the bridges conditioned by their minimum and the excursions of all the diffusion we consider and not just the Brownian motion. Further we describe the Poisson point process of loops…

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