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This article is cited in 6 scientific papers (total in 6 papers)
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
Abstract:
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.
Received in August 2014
Citation:
Alexander Gushchin, Mikhail Urusov, Mihail Zervos, “On the submartingale/supermartingale property of diffusions in natural scale”, Stochastic calculus, martingales, and their applications, Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 287, MAIK Nauka/Interperiodica, Moscow, 2014, 129–139; Proc. Steklov Inst. Math., 287:1 (2014), 122–132
Linking options:
https://www.mathnet.ru/eng/tm3587https://doi.org/10.1134/S0371968514040086 https://www.mathnet.ru/eng/tm/v287/p129
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