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May 2013 The solution of the perturbed Tanaka-equation is pathwise unique
Vilmos Prokaj
Ann. Probab. 41(3B): 2376-2400 (May 2013). DOI: 10.1214/11-AOP716

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.

Citation

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Vilmos Prokaj. "The solution of the perturbed Tanaka-equation is pathwise unique." Ann. Probab. 41 (3B) 2376 - 2400, May 2013. https://doi.org/10.1214/11-AOP716

Information

Published: May 2013
First available in Project Euclid: 15 May 2013

zbMATH: 1284.60134
MathSciNet: MR3098074
Digital Object Identifier: 10.1214/11-AOP716

Subjects:
Primary: 60G44, 60H20, 60J65
Secondary: 60H10, 60J55

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 3B • May 2013
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