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Variational Principles for Asymptotic Variance of General Markov Processes

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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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Acknowledgements

The authors would like to thank the reviewers for suggestions and helpful comments.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350007, P. R. China

    Lu Jing Huang

  2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, P. R. China

    Yong Hua Mao & Tao Wang

Authors
  1. Lu Jing Huang
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  2. Yong Hua Mao
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  3. Tao Wang
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Corresponding author

Correspondence to Tao Wang.

Additional information

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

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