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Itô’s formula for stochastic integration in Banach spaces. (English) Zbl 0737.60043

Diffusion processes and related problems in analysis, Vol. I: Diffusions in analysis and geometry, Proc. Int. Conf., Evanston/IL (USA) 1989, Prog. Probab. 22, 349-397 (1990).
[For the entire collection see Zbl 0716.00011.]
The authors complete with this paper their program of extending stochastic integration to Banach space valued processes. The paper explains the necessary prerequisites from functional analysis (a very useful feature since the techniques used are not familiar to probabilists), and ends with a complete Itô formula, for which the authors must postulate, however, the existence of a suitable quadratic variation.

MSC:

60H05 Stochastic integrals
46G10 Vector-valued measures and integration
60B05 Probability measures on topological spaces

Citations:

Zbl 0716.00011
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