On weak uniqueness for some degenerate SDEs by global $L^p$ estimates
Probability
2014-09-03 v3 Analysis of PDEs
Abstract
We prove uniqueness in law for possibly degenerate SDEs having a linear part in the drift term. Diffusion coefficients corresponding to non-degenerate directions of the noise are assumed to be continuous. When the diffusion part is constant we recover the classical degenerate Ornstein-Uhlenbeck process which only has to satisfy the H\"ormander hypoellipticity condition. In the proof we use global -estimates for hypoelliptic Ornstein-Uhlenbeck operators recently proved in Bramanti-Cupini-Lanconelli-Priola (Math. Z. 266 (2010)) and adapt the localization procedure introduced by Stroock and Varadhan. Appendix contains a quite general localization principle for martingale problems.
Keywords
Cite
@article{arxiv.1305.7174,
title = {On weak uniqueness for some degenerate SDEs by global $L^p$ estimates},
author = {Enrico Priola},
journal= {arXiv preprint arXiv:1305.7174},
year = {2014}
}