XX: 07, 56-67, LNM 1204 (1986)
PICARD, Jean
Une classe de processus stable par retournement du temps
Retrieve article from Numdam
XXIII: 12, 147-160, LNM 1372 (1989)
PICARD, Jean
Martingales sur le cercle Retrieve article from Numdam
XXV: 18, 196-219, LNM 1485 (1991)
PICARD, Jean
Calcul stochastique avec sauts sur une variété (
Stochastic differential geometry)
It is known from Meyer
1505 that intrinsic Ito integrals have a meaning for continuous semimartingales in a manifold $M$, provided $M$ is endowed with a connection. This is extended here to càdlàg semimartingales. The manifold must be endowed with a richer structure, a ``connector'', mapping $M\times M$ to the tangent bundle, that allows to interpret a jump $(X_{t-},X_t)$ as a tangent vector to $M$ at $X{t-}$; the differential of the connector at the diagonal reduces to a classical torsion-free connection. Introducing torsions leads to a more general ``transporter'', describing how parallel transports should behave at jump times, and reducing to a classical connection for infinitesimal jumps. Discrete-time approximations are established.
Keywords: Semimartingales in manifolds,
Martingales in manifolds,
JumpsNature: Original Retrieve article from Numdam
XLIII: 01, 3-70, LNM 2006 (2011)
PICARD, Jean
Representation formulae for the fractional Brownian motion (
Theory of processes)
Keywords: Fractional Brownian motion,
Brownian motionNature: Original,
Survey
