On the one-sided Tanaka equation with drift
Probability
2011-08-23 v1
Abstract
We study questions of existence and uniqueness of weak and strong solutions for a one-sided Tanaka equation with constant drift \lambda. We observe a dichotomy in terms of the values of the drift parameter: for \lambda\leq 0, there exists a strong solution which is pathwise unique, thus also unique in distribution; whereas for \lambda>0, the equation has a unique in distribution weak solution, but no strong solution (and not even a weak solution that spends zero time at the origin). We also show that strength and pathwise uniqueness are restored to the equation via suitable "Brownian perturbations".
Keywords
Cite
@article{arxiv.1108.4069,
title = {On the one-sided Tanaka equation with drift},
author = {Ioannis Karatzas and Albert N. Shiryaev and Mykhaylo Shkolnikov},
journal= {arXiv preprint arXiv:1108.4069},
year = {2011}
}
Comments
15 pages