Local times in a Brownian excursion

Krishna B. Athreya; Raoul Normand; Vivekananda Roy; Sheng-Jhih Wu

Local times in a Brownian excursion

Probability 2014-10-20 v1

Authors: Krishna B. Athreya , Raoul Normand , Vivekananda Roy , Sheng-Jhih Wu

Abstract

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

Keywords

brownian motion

Cite

@article{arxiv.1410.4643,
  title  = {Local times in a Brownian excursion},
  author = {Krishna B. Athreya and Raoul Normand and Vivekananda Roy and Sheng-Jhih Wu},
  journal= {arXiv preprint arXiv:1410.4643},
  year   = {2014}
}

Comments

8 pages

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