Geodesic
On the submartingale/supermartingale property of diffusions in natural scale
Informatics and Automation, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 129-139 
Alexander Gushchin; Mikhail Urusov; Mihail Zervos. On the submartingale/supermartingale property of diffusions in natural scale. Informatics and Automation, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 129-139. http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

S. Kotani (2006) has characterised the martingale property of a one-dimensional diffusion in natural scale in terms of the classification of its boundaries. We complement this result by establishing a necessary and sufficient condition for a one-dimensional diffusion in natural scale to be a submartingale or a supermartingale. Furthermore, we study the asymptotic behaviour of the diffusion's expected state at time $t$ as $t\to\infty$. We illustrate our results by means of several examples.

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