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.


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


Zbl 0923.34056
Full Text: DOI


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