Regularity of local times of random fields |
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| Authors: | Jiagang Ren Xicheng Zhang |
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| Institution: | a School of Mathematics and Computational Science, Zhongshan University, Guangzhou, Guangdong 510275, PR China
b Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China |
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| Abstract: | In this paper, we study the fractional smoothness of local times of general processes starting from the occupation time formula, and obtain the quasi-sure existence of local times in the sense of the Malliavin calculus. This general result is then applied to the local times of N-parameter d-dimensional Brownian motions, fractional Brownian motions and the self-intersection local time of the 2-dimensional Brownian motion, as well as smooth semimartingales. |
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| Keywords: | Quasi-sure existence Local time N-Parameter d-dimensional Brownian motion Fractional Brownian motion Self-intersection local time Smooth semimartingale |
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