Elliptic Estimates Through Stochastic Analysis

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


Variation of an ODE: linearized ODE determining the Jacobian ma­trix — The control map, its Jacobian — Jacobian of a stochastic flow — Higher derivatives of a stochastic flow — Itô functionals, their differentiability — Malliavin matrix of an Itô functional — Reduced variation of an Itô functional — Reduced vari­ation and regularity in the backward variables — Bismut’s identity — Hörmander’s hypoellipticity theorem.


Vector Field Stochastic Differential Equation Stochastic Analysis Stochastic Calculus Transfer Principle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

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  • Paul Malliavin

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