Large tensor products in analysis and probability. (Les gros produits tensoriels en analyse et en probabilités.) (French) Zbl 0597.60043

Aspects of mathematics and its applications, Collect. Pap. Hon. L. Nachbin, 689-725 (1986).
[For the entire collection see Zbl 0581.00004.]
In this paper the author continues his investigation of martingales with values in manifolds [cf. Semi-martingales sur des variétés, et martingales conformes sur des variétés analytiques complexes. (1980; Zbl 0433.60047); Lect. Notes Math. 850, 413–489 (1981; Zbl 0464.60058) and ibid. 921, 1-150 (1982; Zbl 0482.58034)].
He uses methods of differential geometry and, in particular, tensor products of modules over appropriate rings of functions (e.g. \(C^{\infty}\)-functions), hence the expression ”large tensor products” in the title. His methods enable him to improve and simplify results of his from the papers mentioned above, for example his geometric interpretation of Ito’s formula via 2-tangent vectors (Prop. 2.4). In the last section applications to Stratonovitch processes are discussed.


60G48 Generalizations of martingales
46M05 Tensor products in functional analysis
60H05 Stochastic integrals
58J65 Diffusion processes and stochastic analysis on manifolds