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

Alessandra Faggionato

Stochastic Processes and their Applications, 2009, vol. 119, issue 6, 1765-1791

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.

Keywords: Brownian; motion; Marked; point; processes; Palm-Khinchin; theory; Fluctuation; theory (search for similar items in EconPapers)
Date: 2009
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