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arXiv · 0708.0128

The alternating marked point process of h-slopes of the drifted Brownian motion

A. Faggionato
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Abstract

We show that the slopes between h-extrema of the drifted 1D Brownian motion form a stationary alternating marked point process, extending the result of J. Neveu and J. Pitman for the non drifted case. Our analysis covers the results on the statistics of h-extrema obtained by P. Le Doussal, C. Monthus and D. Fisher via a Renormalization Group analysis and gives a complete description of the slope between h-extrema covering the origin by means of the Palm--Khinchin theory. Moreover, we analyze the behavior of the Brownian motion near its h-extrema.

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A. Faggionato. 2007-08-01. The alternating marked point process of h-slopes of the drifted Brownian motion. https://arxiv.org/abs/0708.0128

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