The solution of the perturbed Tanaka-equation is pathwise unique

• Vilmos Prokaj ^[1]
  1. [1] Eötvös Loránd University

     Eötvös Loránd University

     Hungría

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 3, 2, 2013, págs. 2376-2400
• Idioma: inglés
• DOI: 10.1214/11-AOP716
• Texto completo no disponible (Saber más ...)
• Resumen

  • The Tanaka equation dXt=sign(Xt)dBt 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.