Abstract
We show pathwise uniqueness for a class of degenerate Itô-SDE among all of its weak solutions that spend zero time at the points of degeneracy of the dispersion matrix. Consequently, by the Yamada-Watanabe Theorem and a weak existence result, the pathwise unique solutions can be shown to be strong and to exist. The main tools to show pathwise uniqueness are inequalities associated with maximal functions and a Krylov type estimate derived from elliptic regularity and uniqueness in law.
Funding Statement
The research of Haesung Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2020R1A6A3A01096151).
Acknowledgments
The author would like to thank Professor Gerald Trutnau for helpful discussions and suggestions. Additionally, the author is grateful to the anonymous referee for reviewing the manuscript carefully and providing useful comments to improve the paper.
Citation
Haesung Lee. "On the pathwise uniqueness for a class of degenerate Itô-stochastic differential equations." Osaka J. Math. 60 (3) 533 - 543, July 2023.
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