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arXiv · 1104.0740

The solution of the perturbed Tanaka-equation is pathwise unique

Vilmos Prokaj
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Abstract

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.

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Vilmos Prokaj. 2011-04-05. The solution of the perturbed Tanaka-equation is pathwise unique. https://doi.org/10.1214/11-aop716

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