A Remark on Tsirelson's Stochastic Differential Equation
نویسنده
چکیده
| Tsirelson's stochastic di erential equation is called \celebrated and mysterious" by Rogers and Williams bd16ce. This note aims at making it a little more celebrated and a little less mysterious. Using a deterministic time-change, we translate the study of Tsirelson's equation into the study of \eternal" Brownian motion on the circle. This allows us to show that the ltration generated by any solution of Tsirelson's equation is also generated by some Brownian motion (which, however, cannot be the Brownian motion driving the equation, because the equation has no strong solution).
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