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

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  • Song, Shiyu
  • Wang, Suxin
  • Wang, Yongjin

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.

Suggested Citation

  • Song, Shiyu & Wang, Suxin & Wang, Yongjin, 2016. "On some properties of reflected skew Brownian motions and applications to dispersion in heterogeneous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 90-105.
    • Handle: RePEc:eee:phsmap:v:456:y:2016:i:c:p:90-105
    DOI: 10.1016/j.physa.2016.02.041
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    References listed on IDEAS

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    1. Antoine Lejay & Ernesto Mordecki & Soledad Torres, 2014. "Is a Brownian Motion Skew?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 346-364, June.
    2. Mario Abundo, 2010. "On the First Hitting Time of a One-dimensional Diffusion and a Compound Poisson Process," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 473-490, September.
    3. Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2004. "Applications of δ-function perturbation to the pricing of derivative securities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(3), pages 677-692.
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    Cited by:

    1. Yizhou Bai & Zhiyu Guo, 2019. "An Empirical Investigation to the “Skew” Phenomenon in Stock Index Markets: Evidence from the Nikkei 225 and Others," Sustainability, MDPI, vol. 11(24), pages 1-17, December.

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