Excursions of the Brox Diffusion

Carlos G. Pacheco () and Mariana Pérez-Rojas ()
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Carlos G. Pacheco: CINVESTAV-IPN
Mariana Pérez-Rojas: CINVESTAV-IPN

Journal of Theoretical Probability, 2022, vol. 35, issue 3, 1479-1500

Abstract: Abstract We describe the excursion point process of the so-called Brox diffusion together with the characteristic measure. We do so in terms of the excursion point process of a Brownian motion. To relate these two processes, we make use of the Itô–McKean representation for diffusions and the representation of their local time. As a first application of this analysis, we obtain the distribution of random variables regarding the local time at certain hitting times. At the end, we show an application that illustrates the connection between the paths of the Brox diffusion and the local minima of the environment.

Keywords: Brox diffusion; Excursion theory; Local time; 60K37; 60G17; 60J55; 60J60 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01113-5

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