THE SOLUTION OF THE PERTURBED TANAKA-EQUATION IS PATHWISE UNIQUE

• 成果类型: Article
• 署名作者: Prokaj, Vilmos
• 署名单位: Eotvos Lorand University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP716
• 发表日期: 2013
• 页码: 2376-2400
• 关键词: constant drift

摘要

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.