漂移布朗运动h-斜率的交替标值点过程
The alternating marked point process of h-slopes of the drifted Brownian motion
摘要：
证明了漂移一维布朗运动的h-极值之间的斜率形成一个平稳的交替标值点过程，推广了J. Neveu和J. Pitman关于非漂移情形的结果.我们的分析覆盖了P. Le Doussal，C. Monthus和D. Fisher通过重正化群分析给出了一个新的方法，并通过Palm-Khinchin理论给出了覆盖原点的h-极值之间的斜率的完整描述。此外，我们分析了布朗运动在其h-极值附近的行为。
英文摘要：
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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