The solution of the perturbed Tanaka--equation is pathwise unique

Details The solution of the perturbed Tanaka--equation is pathwise unique The solution of the perturbed Tanaka--equation is pathwise unique

2011-04-05

arxiv.org/abs/1104.0740v2

Mathematics

Probability

Mostly correction of typos

Scientific paper

The Tanaka equation $dX_t=\sign(X_t)dB_t$ 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.

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