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Géométrie différentielle stochastique (bis). (English) Zbl 0539.58039

Séminaire de probabilités XVI, Univ. Strasbourg 1980/81, Suppl.: Géométrie différentielle stochastique, Lect. Notes Math. 921, 165-207 (1982).
[For the entire collection see Zbl 0471.00024.]
This paper is an introductory account of the theory of stochastic differential equations driven by continuous semimartingales, taking values in a differentiable manifold. The reader is assumed to have read the author’s expository article in Séminaire de probabilités XV, Univ. Strasbourg 1979/80, Lect. Notes Math. 850, 44-102 (1981; Zbl 0459.60046). The principal topics covered here are: Stratonovich s.d.e’s and their geodesic approximation; geodesic correction to parallel transport; linear s.d.e’s and connections on the tangent bundle; local characteristics of semimartingales, and ”stochastic differentiation” with respect to a connection; Nelson’s stochastic mechanics.
Reviewer: R.Darling

MSC:

58J65 Diffusion processes and stochastic analysis on manifolds
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60J65 Brownian motion
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