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Lévy area of Wiener processes in Banach spaces. (English) Zbl 1016.60071
The second author has recently developed a new approach to an equation \(dy = f(y)dx\) in the Euclidean space, applicable also in the case when \(x\) is a non-smooth function, like a trajectory of a Brownian motion [see e.g., Rev. Mat. Iberoam. 14, 215-310 (1998; Zbl 0923.34056), or the book by the second and the third author, “System control and rough paths” (Oxford, 2002)]. In the paper it is shown that this theory covers also equations driven by Banach space-valued Wiener processes, which implies that the classical Stratonovich integration theory may be extended to Wiener processes in Banach spaces.

MSC:
60J65 Brownian motion
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G15 Gaussian processes
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