An anticipated calculus on a compact Riemannian manifold. (Un calcul anticipatif sur une variété riemannienne compacte.) (French) Zbl 0794.58047
Körezlioǧlu, H. (ed.) et al., Stochastic analysis and related topics. Boston: Birkhäuser. Prog. Probab. 31, 211-235 (1992).
The authors consider random variables defined on a Wiener space, and with values in a manifold or in the tangent bundle of this manifold. They define the stochastic differentiation for such variables in a way which extends the case of real-valued variables. Then, by considering the adjoint of this differentiation operator, they construct the Skorokhod integral of a process which is tangent to some random time-independent point of the manifold. Finally, a formula which gives the covariance of two Skorokhod integrals and which involves the curvature of the manifold is proved.
For the entire collection see [Zbl 0777.00015].
For the entire collection see [Zbl 0777.00015].
Reviewer: J.Picard (Aubière)
MSC:
58J65 | Diffusion processes and stochastic analysis on manifolds |
60H07 | Stochastic calculus of variations and the Malliavin calculus |