@article{ECP1665,
author = {Ioannis Karatzas and Albert Shiryaev and Mykhaylo Shkolnikov},
title = {On the one-sided Tanaka equation with drift},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {16},
year = {2011},
keywords = {Stochastic differential equation, weak existence, weak uniqueness, strong existence, strong uniqueness, Tanaka equation, skew Brownian motion, sticky Brownian motion, comparison theorems for diffusions},
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".},
pages = {no. 58, 664-677},
issn = {1083-589X},
doi = {10.1214/ECP.v16-1665},
url = {http://ecp.ejpecp.org/article/view/1665}}