On the one-sided Tanaka equation with drift

Details On the one-sided Tanaka equation with drift On the one-sided Tanaka equation with drift

2011-08-19

arxiv.org/abs/1108.4069v1

Mathematics

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15 pages

Scientific paper

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".

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