Local times in a Brownian excursion

2014/10/17 by Krishna B. Athreya, Raoul Normand, Athreya, Krishna B. +5
Mathematics · #FOS: Mathematics #Primary: 60J65 #Probability (math.PR) #Secondary: 60F05 #math.PR #msc:60F05 #msc:60J65

paper · pdf · doi:10.48550/arxiv.1410.4643

8 pages

arxiv created 2014/10/17 · arxiv updated 2014/10/20

Abstract

Let \B(t), t ≥ 0\ be a standard Brownian motion in ℝ. Let T be the first return time to 0 after hitting 1, and \L(T,x), x ∈ ℝ\ be the local time process at time T and level x. The distribution of L(T,x) for each x ∈ ℝ is determined. This is applied to the estimation of a L¹ integral on ℝ.

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