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The Lévy area process for the free Brownian motion. (English) Zbl 0979.60044
A Lévy area process for the free Brownian motion and a typical geometric rough path, laying above the free Brownian path, are constructed. The general result of T. J. Lyons [Rev. Mat. Iberoam. 14, No. 2, 215-310 (1998; Zbl 0923.34056)] is applied to the free Brownian motion case.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
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