Abstract
In this paper, we establish the Hausdorff dimensions of inverse images and collision time sets for a large class of symmetric Markov processes on metric measure spaces. We apply the approach in the works by Hawkes and Jain–Pruitt, and make full use of heat kernel estimates. In particular, the results efficiently apply to symmetric diffusion processes, symmetric stable-like processes, and symmetric diffusion processes with jumps in d-sets.
Acknowledgments
The authors would like to thank the referee for helpful suggestions, which led to the improvement of this paper. Thanks are also due to Professor Zhen-Qing Chen for informing [4] to the authors. The research of Yuichi Shiozawa is supported by JSPS KAKENHI Grant Numbers 22K18675, 23H01076. The research of Jian Wang is supported by the National Key R&D Program of China (2022YFA1006003) and NSF of China (Nos. 11831014, 12071076 and 12225104).
Citation
Yuichi Shiozawa. Jian Wang. "Hausdorff dimensions of inverse images and collision time sets for symmetric Markov processes." Electron. J. Probab. 29 1 - 56, 2024. https://doi.org/10.1214/23-EJP1069
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