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

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  • Faggionato, Alessandra

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.

Suggested Citation

  • Faggionato, Alessandra, 2009. "The alternating marked point process of h-slopes of drifted Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1765-1791, June.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:6:p:1765-1791
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