On the pathwise uniqueness for a class of degenerate It\^{o}-stochastic differential equations
Probability
2022-05-24 v3
Abstract
We show pathwise uniqueness for a class of degenerate It\^{o}-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.
Keywords
Cite
@article{arxiv.2108.04713,
title = {On the pathwise uniqueness for a class of degenerate It\^{o}-stochastic differential equations},
author = {Haesung Lee},
journal= {arXiv preprint arXiv:2108.04713},
year = {2022}
}
Comments
12 pages, typo corrected, some content added