Quasi sure analysis of local times of anticipating smooth semimartingales |
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| Authors: | Guilan Cao Kai He |
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| Affiliation: | a Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China
b Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, PR China |
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| Abstract: | Let  be the anticipating smooth semimartingale and  be its generalized local time. In this paper, we give some estimates about the quasi sure property of Xt and its quadratic variation process t〈X〉. We also study the fractional smoothness of  and prove that the quadratic variation process of  can be constructed as the quasi sure limit of the form  , where  is a sequence of subdivisions of [a,b],  , i=0,1,…,n2. |
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| Keywords: | 60H07 60G44 31C15 31C25 |
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