Corrections for "Occupation and local times for skew Brownian motion with applications to dispersion across an interface"

TL;DR

This paper provides corrections to a previous study on skew Brownian motion, clarifying the conditions under which certain formulas and interpretations are valid, and rectifying computational errors in key results.

Contribution

The authors correct and clarify previous results on occupation and local times for skew Brownian motion, removing unnecessary restrictions and fixing computational errors.

Findings

The restriction of gamma to non-negative values in Theorem 1.3 is unnecessary.

Corrected formulas in Corollary 3.3 are provided.

Probabilistic interpretation of results holds only when gamma is non-negative.

Abstract

We are making corrections and acknowledging colleagues that pointed out mistakes in our recent paper titled "Occupation and local times for skew Brownian motion with applications to dispersion across an interface" which was published in Annals of Applied Probability (2011) 21(1) 183-214. Specifically the corrections are: 1. The restriction of $\gamma$ to non negative values in Theorem 1.3 is not needed. But one has probabilistic interpretation only when $\gamma$ is non negative. 2. State the correct formulas in Corollary 3.3 as their were computational errors in the original formulas. We thank Pierre Etoir\'e and Miguel Martinez for pointing out these errors.