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Эта публикация цитируется в 6 научных статьях (всего в 6 статьях)
On the submartingale/supermartingale property of diffusions in natural scale
Alexander Gushchina, Mikhail Urusovb, Mihail Zervosc a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b Faculty of Mathematics, University of Duisburg-Essen, Essen, Germany
c Department of Mathematics, London School of Economics, London, UK
Аннотация:
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.
Поступило в августе 2014 г.
Образец цитирования:
Alexander Gushchin, Mikhail Urusov, Mihail Zervos, “On the submartingale/supermartingale property of diffusions in natural scale”, Стохастическое исчисление, мартингалы и их применения, Сборник статей. К 80-летию со дня рождения академика Альберта Николаевича Ширяева, Труды МИАН, 287, МАИК «Наука/Интерпериодика», М., 2014, 129–139; Proc. Steklov Inst. Math., 287:1 (2014), 122–132
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/tm3587https://doi.org/10.1134/S0371968514040086 https://www.mathnet.ru/rus/tm/v287/p129
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