The solution of the perturbed Tanaka-equation is pathwise unique
Probability
2013-07-12 v3
Abstract
The Tanaka equation 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.
Cite
@article{arxiv.1104.0740,
title = {The solution of the perturbed Tanaka-equation is pathwise unique},
author = {Vilmos Prokaj},
journal= {arXiv preprint arXiv:1104.0740},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AOP716 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)