Abstract
By using the coupling method and the localization technique, we establish non-uniform gradient estimates for Markov semigroups of diffusions or stochastic differential equations driven by pure jump Lévy noises, where the coefficients only satisfy local monotonicity conditions.
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The authors would like to thank the two referees for numerous corrections.
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Supported by the National Natural Science Foundation of China (Grant No. 11831014), the Program for Probability and Statistics: Theory and Application (Grant No. IRTL1704) and the Program for Innovative Research Team in Science and Technology in Fujian Province University (IRTSTFJ)
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Wang, J., Wu, B.Y. Non-uniform Gradient Estimates for SDEs with Local Monotonicity Conditions. Acta. Math. Sin.-English Ser. 37, 458–470 (2021). https://doi.org/10.1007/s10114-020-9365-6
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DOI: https://doi.org/10.1007/s10114-020-9365-6
Keywords
- Gradient estimate
- Markov semigroup
- monotonicity condition
- coupling
- stochastic differential equation
- Lévy process