On some properties of reflected skew Brownian motions and applications to dispersion in heterogeneous media

Shiyu Song, Suxin Wang and Yongjin Wang

Physica A: Statistical Mechanics and its Applications, 2016, vol. 456, issue C, 90-105

Abstract: Motivated by the close connection between the skew Brownian motion and the random particle motion in heterogeneous media, we investigate the reflected skew Brownian motion and try to find out its relationship with the corresponding dispersion problem when there exists a reflecting boundary. Through the use of the knowledge of stochastic analysis, we provide some basic properties of reflected skew Brownian motions, including the transition density, the Laplace transform of the first passage time, and some related results. A simple method to generate the sample path is also proposed. At the end of this paper, we reveal the strong relationship between the reflected skew Brownian motion and the solute dispersion in the presence of a sharp interface and a reflecting boundary.

Keywords: Reflected skew Brownian motion; Transition density; First passage time; Simulation; Physical reflected skew diffusion; Heterogeneous media (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:456:y:2016:i:c:p:90-105

DOI: 10.1016/j.physa.2016.02.041

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