Tanaka's equation is the one-dimensional stochastic differential equation driven by canonical Brownian motion B, with initial condition X0 = 0, where sgn denotes the sign function (Note the unconventional value for sgn(0).)
The signum function does not satisfy the Lipschitz continuity condition required for the usual theorems guaranteeing existence and uniqueness of strong solutions.
However, the Tanaka equation does have a weak solution, one for which the process X and version of Brownian motion are both specified as part of the solution, rather than the Brownian motion being given a priori.
In this case, simply choose X to be any Brownian motion and define
Another counterexample of this type is Tsirelson's stochastic differential equation.