Abstract
In the present paper, we study an upper escape rate of some time inhomogeneous diffusion process associated with a family of regular and local Dirichlet forms. In particular, by making full use of Gaussian type’s heat kernel estimates, we establish integral tests for an upper rate function of the time inhomogeneous diffusion process with a coefficient that is not necessarily bounded concerning space and time.
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Acknowledgements
The authors would like to thank the referee for his/her valuable comments and suggestions. The first named author is partially supported by JSPS KAKENHI Grant number 20K03635.
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Japan Society for the Promotion of Science, 20K03635.
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Daehong Kim and Yoichi Oshima wrote and reviewed the manuscript.
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Kim, D., Oshima, Y. On the Upper Rate Functions of Some Time Inhomogeneous Diffusion Processes. Potential Anal 60, 1181–1213 (2024). https://doi.org/10.1007/s11118-023-10083-8
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DOI: https://doi.org/10.1007/s11118-023-10083-8
Keywords
- Upper rate function
- Time inhomogeneous diffusion process
- Heat kernel estimate
- Time dependent Dirichlet form.