SOME BASIC PROPERTIES OF THE NOISE REINFORCED BROWNIAN MOTION

Abstract

Noise reinforced Brownian motion appears as the universal limit of the step reinforced random walk. This article aims to study some basic properties of the noise reinforced Brownian motion. As main results, we prove integral representation, series expansion, Markov property, and martingale property of the noise reinforced Brownian motion.

Keywords

• noise reinforced brownian motion
• integral representation
• markov property
• martingale property