On the pathwise uniqueness for a class of degenerate Itô-stochastic differential equations
arXiv:2108.04713
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.
arXiv comment12 pages, typo corrected, some content added