Path decomposition of a spectrally negative L\'evy process, and local time of a diffusion in this environment

Grégoire Véchambre

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arXiv · 1605.05084

Path decomposition of a spectrally negative L\'evy process, and local time of a diffusion in this environment

Grégoire Véchambre

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Abstract

We study the convergence in distribution of the supremum of the local time and of the favorite site for a transient diffusion in a spectrally negative L\'evy potential. To do so, we study the h-valleys of a spectrally negative L\'evy process, and we prove in partiular that the renormalized sequence of the h-minima converges to the jumping times sequence of a standard Poisson process.

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Grégoire Véchambre. 2016-05-17. Path decomposition of a spectrally negative L\'evy process, and local time of a diffusion in this environment. https://arxiv.org/abs/1605.05084

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