A short review on boundary behavior of linear diffusion processes

Noureddine Jilani Ben Naouara and Faouzi Trabelsi – GJM, Volume 1, Issue 2 (2016), 138-149.

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We present in a complete and synthetic way the modern classification of boundaries of one dimensional diffusion process. This classification is proved using the scale function as well as the speed measure associated to a one dimensional diffusion. In order to highlight the behavior of a diffusion process, we follow a numerical approach with graphical illustrations. To this end, different schemes are used to approximate the paths of a diffusion process such as Euler Maruyama and Milstein, which will be used to approximate Wright-Fisher diffusion process near to Exit, regular, entrance, or natural boundaries. Finally, we offer well-organized tables on the nature of any boundary (closed or open) of a given sub-interval of the state space, with appropriate conditions. We believe that these contributions are very useful to better understand the physical and natural meaning of boundary classification.

Milestones:

Received: June 2016
Published online: December 2016

Authors:

Noureddine Jilani Ben Naouara
Université de Monastir
Département de Mathématique
Avenue de l'Environnement, 5000 Monastir - Tunisia
Faouzi Trabelsi
Université de Monastir
Département de Mathématique,
Avenue de la Corniche, B.P. 223,
5000 Monastir, Tunisia

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