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Zbl 0654.60040
Pratelli, Maurizio
Integration stochastique et geometrie des espaces de Banach. (Stochastic integration and geometry of Banach spaces). (French)
[A] Séminaire de probabilités XXII, Strasbourg/France, Lect. Notes Math. 1321, 129-137 (1988).

[For the entire collection see Zbl 0635.00013.] \par This paper investigates the relationship between the stochastic integration for Banach-valued processes and the geometry of Banach spaces. It is shown in particular that a reasonable stochastic integral of the form $\int X\sb sdM\sb s$, where $M\sb s$ is an F-valued martingale and $X\sb s$ a predictable process with values in ${\cal L}(F,G)$, can be made if the Banach space F is 2-uniformly convex and G is 2-uniformly smooth.
[M.Pratelli]

MSC 2000:: *60H05 Stochastic integrals
60B05 Probability measures on topological spaces
60G44 Martingales with continuous parameter

Keywords: stochastic integration for Banach-valued processes; geometry of Banach spaces

Citations: Zbl 0635.00013

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