An Invitation to Second-Order Stochastic Differential Geometry

Michel Emery (1)

1 IRMA - Institut de Recherche Mathématique Avancée

These lectures given at the Dimitsana Summer School in July 2005 provide an introduction to second-order differential geometry and its use for intrinsic stochastic calculus in differentiable manifolds. This language, due to L. Schwartz and P.A. Meyer, allows an intrinsic description of semimartingales, stochastic integrals and stochastic differential equations in manifolds. Two first-order calculi arise as particular instances of this point of view: the well known intrinsic Stratonovich calculus and the less familiar intrinsic Itô calculus in manifolds.

Mots clés: Stochastic differential geometry; Second-order differential geometry; Stochastic calculus in manifolds

Domaines: Probabilités [math.PR]; Géométrie différentielle [math.DG]

Michel Emery. An Invitation to Second-Order Stochastic Differential Geometry. 2007. ⟨hal-00145073⟩