A remark on Tsirelson's stochastic differential equation.

Michel Emery (1) , Walter Schachermayer

1 IRMA - Institut de Recherche Mathématique Avancée

A deterministic time-change translates the study of Tsirelson's famous stochastic differential equation with no strong solution into the study of ``eternal'' Brownian motion on a circle. This bypass and a coupling argument show that the filtration generated by a solution to the equation is also generated by some Brownian motion (containing more information than the Brownian motion that drives the equation).

Mots clés: "stochastic differential equation; weak solutions of stochastic differential equations; Brownian filtration"; stochastic differential equation; Brownian filtration

Domaines: Probabilités [math.PR]

Michel Emery, Walter Schachermayer. A remark on Tsirelson's stochastic differential equation.. 1998. ⟨hal-00129583⟩