Rough linear PDE's with discontinuous coefficients - existence of solutions via regularization by fractional Brownian motion
Probability
2018-06-26 v3
Abstract
We consider two related linear PDE's perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a regularizing effect on the equations in the sense that we can prove existence of solutions for almost all paths of the fractional Brownian motion.
Keywords
Cite
@article{arxiv.1509.01154,
title = {Rough linear PDE's with discontinuous coefficients - existence of solutions via regularization by fractional Brownian motion},
author = {Torstein Nilssen},
journal= {arXiv preprint arXiv:1509.01154},
year = {2018}
}
Comments
v2: change in definition 5.1 v3: corrected error regarding strong local non-determinism. Merged together with arXiv:1512.07274