%0 Journal Article
%T The solution of the perturbed Tanaka-equation is pathwise unique
%A Vilmos Prokaj
%J Mathematics
%D 2011
%I arXiv
%R 10.1214/11-AOP716
%X The Tanaka equation $dX_t={\operatorname{sign}}(X_t)\,dB_t$ is an example of a stochastic differential equation (SDE) without strong solution. Hence pathwise uniqueness does not hold for this equation. In this note we prove that if we modify the right-hand side of the equation, roughly speaking, with a strong enough additive noise, independent of the Brownian motion B, then the solution of the obtained equation is pathwise unique.
%U http://arxiv.org/abs/1104.0740v3