On the increments of the principal value of Brownian local time

2005/01/13 by Endre Csáki, Csáki, Endre, Yueyun Hu +1
Economics, Econometrics and Finance · Mathematics · #60F15 #60J55 #60J65 #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60F15 #msc:60J55 #msc:60J65

paper · pdf · doi:10.48550/arxiv.math/0501199

23 pages

arxiv created 2005/01/13 · openalex publication_date 2005/01/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let W be a one-dimensional Brownian motion starting from 0. Define Y(t)= ∫₀^t\d s \over W(s) := lim_ε→0 ∫₀^t 1_{(|W(s)|> ε)} \d s \over W(s) as Cauchy's principal value related to local time. We prove limsup and liminf results for the increments of Y.

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