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A complete differential formalism for stochastic calculus in manifolds. (English) Zbl 0791.58111

Séminaire de probabilités XXVI, Lect. Notes Math. 1526, 189-209 (1992).
[For the entire collection see Zbl 0754.00008.]
In this essay the point of view that the stochastic calculus on manifolds has two main roles – to construct new processes from old and to determine martingales – is developed. This is done by using covariant stochastic differentials of processes in vector bundles. When these covariant differentials are introduced the formalism becomes as flexible and as complete as in the real-valued case.

MSC:

58J65 Diffusion processes and stochastic analysis on manifolds

Citations:

Zbl 0754.00008
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