Complete lifts of connections and stochastic Jacobi fields
by Marc Arnaudon and Anton Thalmaier

Differentiable families of -martingales on manifolds are investigated: their infinitesimal variation provides a notion of stochastic Jacobi fields. Such objects are known to be martingales taking values in the tangent bundle when the latter is equipped with the complete lift of the connection . We discuss various characterizations of TM-valued martingales and apply our results to establish formulas in connection with the stochastic representation of the heat flow for harmonic maps between Riemannian manifolds. As an application, we give local and global gradient estimates for harmonic maps of bounded dilatation.

J. Math. Pures Appl. 77 (1998) 283-315 [ORIGINAL ARTICLE]

The paper is available here:

Marc Arnaudon <>
Anton Thalmaier <>

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