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On the submartingale / supermartingale property of diffusions in natural scale
P. 129-139.
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 $t \rightarrow \infty$. We illustrate our results by means of several examples.
Language:
English
In book
Т. 287: Стохастическое исчисление, мартингалы и их применения: Сборник статей. К 80-летию со дня рождения академика Альберта Николаевича Ширяева. , М. : МАИК, 2014