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De nouveaux résultats sur l’équation de Tsirel’son. (Some new results on Tsirel’son’s equation). (French) Zbl 0697.60062
The following equation with respect to \((\eta_ k)\) is considered: \[ d\eta_ k=\xi_ k+\{\eta_ k\}, \] where \((\xi_ k)\) is a given sequence of independent r.v. with a corresponding sequence of one- dimensional distributions \(\mu =(\mu_ k)\), \(\{\) \(\cdot \}\) is a fraction part. An equation of this type has been used by Tsirelson to construct his famous example on nonexistence of strong solutions for SDEs.
Let \(P_{\mu}\) be a set of distributions of solutions. Several results on the structure of \(P_{\mu}\) are obtained. In particular, an answer to the question when \(P_{\mu}\) contains a single point is given.
Reviewer: Yu.M.Kabanov

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)