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A remark on Tsirelson’s stochastic differential equation. (English) Zbl 0957.60064

Azéma, Jacques (ed.) et al., Séminaire de probabilités XXXIII. Berlin: Springer. Lect. Notes Math. 1709, 291-303 (1999).
Tsirelson’s equation (T) is an SDE with constant diffusion coefficient whose solutions are not adapted to the natural filtration of the driving Brownian motion. The authors give a new explanation of this phenomenon: They exhibit via time change and coupling a 1-1 correspondence between the solution of (T) to a stationary circular Brownian motion. For the latter the difference between the innovation filtration and the natural filtration is a simple and well known fact.
For the entire collection see [Zbl 0924.00016].

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G07 General theory of stochastic processes
60G35 Signal detection and filtering (aspects of stochastic processes)
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