On a Brownian motion with a hard membrane

Abstract

Local perturbations of a Brownian motion are considered. As a limit we obtain a non-Markov process that behaves as a reflected Brownian motion on the positive half line until its local time at zero reaches some exponential level, then changes a sign and behaves as a reflected Brownian motion on the negative half line until some stopping time, etc.

9 pages

References in corpus (2)

• On the constructions of the skew Brownian motion
• Lorentz Process with shrinking holes in a wall

Cited by in corpus (2)

• Gene flow across geographical barriers - scaling limits of random walks with obstacles
• Limit behaviour of random walks on ${\mathbb{Z}}^m$ with two-sided membrane