Smoothness of Laws

  • Paul Malliavin
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 313)


Divergence of differentiable flow — Divergence as the adjoint operator of a derivation — Non-degenerate maps and their covariance matrices — Lifting up vector fields through a non-degenerate map — Pushing down divergences — Hölder regularity under D 2 ∞−0 hypothesis — Smoothness under D hypothesis — Lifting up and pushing down through a non-degenerate D map — Inverse image of a distribution — Absolute continuity of scalar functionals under D 1 1 hypothesis — Appendix: Computation of derivatives by means of divergence operators — Law of a weakly non degenerated map.


Vector Field Lebesgue Measure Conditional Expectation Inverse Image Absolute Continuity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

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  • Paul Malliavin

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