On a Condition that One-Dimensional Diffusion Processes are Martingales
On a Condition that One-Dimensional Diffusion Processes are Martingales
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DOI：
10.1007/978-3-540-35513-7_12
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
S. Kotani
中科院分区：
文献类型：
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作者：
S. Kotani
It is surprising that there are examples of local martingales {Xt} which are not martingales in spite of the existence of all moments ([6]). Recently there have been several works linking the tail probability of the quadratic variation {〈 X〉 t} to that of the maximum process {sups 妻 t Xs}([2],[3],[7]). In this note we give a necessary and sufficient condition for one-dimensional diffusion processes to be martingales.On an interval (l−, l+) with−∞⩽ l−< l+⩽+∞, let m (dx) be a non-negative measure satisfying m (I)> 0 for any non-empty open interval I⊂(l−, l+). Denote the minimal diffusion process with speed measure m (dx) and scale function s (x)= x by