Abstract
We provide a framework for studying the expansion rate of the image of a bounded set under a semi-flow in Euclidean space and apply it to stochastic differential equations (SDEs for short) with singular coefficients. If the singular drift of the SDE can be split into two terms, one of which is singular and the radial component of the other term is negative then, under suitable conditions, the random dynamical system generated by the SDE admits a pullback attractor.
Funding Statement
CL is supported by the DFG through the research unit (Forschergruppe) FOR 2402 and the Austrian Science Fund (FWF) Stand-Alone programme P 34992.
Acknowledgments
Inspiring suggestion from and fruitful discussions with Benjamin Gess (Bielefeld) are appreciated. Discussions with Xicheng Zhang (Beijing) and Zimo Hao (Bielefeld) are acknowledged. We thank both the associate editor and one of the referees for very useful comments and suggestions.
Citation
Chengcheng Ling. Michael Scheutzow. "Expansion and attraction of RDS: long time behavior of the solution to singular SDE." Electron. J. Probab. 29 1 - 33, 2024. https://doi.org/10.1214/24-EJP1118
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