Path decomposition of a spectrally negative Lévy process, and local time of a diffusion in this environment

2016/05/17 by Grégoire Véchambre, Véchambre, Grégoire
Decision Sciences · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1605.05084

openalex publication_date 2016/05/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 Lévy potential. To do so, we study the h-valleys of a spectrally negative Lévy 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.

Citations

• Exponential functionals of spectrally one-sided l 'evy processes\n conditioned to stay positive

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