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Pré-Publication, Document De Travail Année : 2017

THE REGULARITY OF THE LINEAR DRIFT IN NEGATIVELY CURVED SPACES

François Ledrappier
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Lin Shu
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Résumé

We show the linear drift of the Brownian motion on the universal cover of a closed connected Riemannian manifold is C k´2 differentiable along any C k curve in the manifold of C k metrics with negative sectional curvature. We also show that the stochastic entropy of the Brownian motion is C 1 differentiable along any C 3 curve of C 3 metrics with negative sectional curvature. We formulate the first derivatives of the linear drift and entropy, respectively, and show they are critical at locally symmetric metrics.
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Dates et versions

hal-01630521 , version 1 (07-11-2017)
hal-01630521 , version 2 (11-05-2018)

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  • HAL Id : hal-01630521 , version 1

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François Ledrappier, Lin Shu. THE REGULARITY OF THE LINEAR DRIFT IN NEGATIVELY CURVED SPACES. 2017. ⟨hal-01630521v1⟩
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