Abstract
A variational formula for the asymptotic variance of general Markov processes is obtained. As application, we get an upper bound of the mean exit time of reversible Markov processes, and some comparison theorems between the reversible and non-reversible diffusion processes.
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The authors would like to thank the reviewers for suggestions and helpful comments.
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Supported by NSFC (Grant No. 11901096), NSF-Fujian (Grant No. 2020J05036), the Program for Probability and Statistics: Theory and Application (Grant No. IRTL1704), the Program for Innovative Research Team in Science and Technology in Fujian Province University (IRTSTFJ), the National Key R&D Program of China (2020YFA0712900 and 2020YFA0712901), and the National Natural Science Foundation of China (Grant No. 11771047)
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Huang, L.J., Mao, Y.H. & Wang, T. Variational Principles for Asymptotic Variance of General Markov Processes. Acta. Math. Sin.-English Ser. 39, 107–118 (2023). https://doi.org/10.1007/s10114-022-1226-z
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DOI: https://doi.org/10.1007/s10114-022-1226-z
Keywords
- Markov process
- asymptotic variance
- variational formula
- the mean exit time
- comparison theorem
- semi-Dirichlet form