DIMENSION RESULTS FOR ORNSTEIN-UHLENBECK TYPE MARKOV PROCESS |
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| Institution: | 1. Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel;2. Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel;3. Max-Planck Institute for the Physics of Complex Systems, Dresden D-01187, Germany |
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| Abstract: | Let {Xt, t ≥ 0} be an Ornstein-Uhlenbeck type Markov process with Levy process At, the authors consider the fractal properties of its ranges, give the upper and lower bounds of the Hausdorff dimensions of the ranges and the estimate of the dimensions of the level sets for the process. The existence of local times and occuption times of Xt are considered in some special situations. |
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| Keywords: | Levy process Ornstein-Uhlenbeck type Markov process range level set Hausdorff dimension local time occuption time 60G17 60J25 |
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