XVI-S: 55, 1-150, LNM 921 (1982)
SCHWARTZ, Laurent
Géométrie différentielle du 2ème ordre, semi-martingales et équations différentielles stochastiques sur une variété différentielle
Retrieve article from Numdam
XVI-S: 56, 151-164, LNM 921 (1982)
MEYER, Paul-André
Variation des solutions d'une e.d.s., d'après J.M. Bismut Retrieve article from Numdam
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
3214Keywords: Semimartingales in manifolds,
Stochastic differential equations,
Local characteristics,
Nelson's stochastic mechanics,
Transfer principleNature: Original Retrieve article from Numdam
XVI-S: 58, 208-216, LNM 921 (1982)
ÉMERY, Michel
En marge de l'exposé de Meyer : ``Géométrie différentielle stochastique'' (
Stochastic differential geometry)
Marginal remarks to Meyer
1657Keywords: Semimartingales in manifolds,
Stochastic differential equationsNature: Original Retrieve article from Numdam
XVI-S: 59, 217-236, LNM 921 (1982)
DARLING, Richard W.R.
Martingales in manifolds - Definition, examples and behaviour under maps (
Stochastic differential geometry)
Martingales in manifolds have been introduced independently by Meyer
1505 and the author (Ph.D. Thesis). This short note is a review of that thesis; here, the definition of a manifold-valued martingale is by its behaviour under convex functions
Comment: More details are given in
Bull. L.M.S. 15 (1983),
Publ R.I.M.S. Kyoto~
19 (1983) and
Zeit. für W-theorie 65 (1984). Characterizating of manifold-valued martingales by convex functions has become a powerful tool: see for instance Émery's book
Stochastic Calculus in Manifolds (Springer, 1989) and his St-Flour lectures (Springer LNM 1738)
Keywords: Martingales in manifolds,
Semimartingales in manifolds,
Convex functionsNature: Original Retrieve article from Numdam
XVI-S: 60, 237-284, LNM 921 (1982)
AZENCOTT, Robert
Formule de Taylor stochastique et développement asymptotique d'intégrales de Feynman Retrieve article from Numdam
