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XVI-S: 57, 165-207, LNM 921 (1982)
MEYER, Paul-André
Géométrie différentielle stochastique (bis) (Stochastic differential geometry)
A sequel to 1505. The main theme is that an ordinary differential equation has a non unique extension as a stochastic differential equation: besides the Stratonovich one, given by the ``transfer principle'', there are other possibilities: choosing among them requires some additional, connection-like, structure. The most striking application is the Dohrn-Guerra correction to the parallel transport along a semimartingale
Comment: For complements, see Émery 1658, Hakim-Dowek-Lépingle 2023, Émery's monography Stochastic Calculus in Manifolds (Springer, 1989) and article 2428, and Arnaudon-Thalmaier 3214
Keywords: Semimartingales in manifolds, Stochastic differential equations, Local characteristics, Nelson's stochastic mechanics, Transfer principle
Nature: Original
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