From Ordinary Differential Equations to Stochastic Flow: The Transfer Principle

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


Stratonovich SDE — Intrinsic stochastic integral — Itô SDE, uniqueness of the Cauchy problem — The Stroock-Varadhan piecewise linear approximation — Algebraic analysis on the group of C-diffeomorphisms: the exponential map, the adjoint action — Reduced variation of the Stroock-Varadhan approximation sequence of a smooth SDE, its a priori bound; Bootstrap and proof of the limit theorem — Cauchy problem for SDE with Lipschitz coefficients — Critique of our approach.


Ordinary Differential Equation Vector Field Cauchy Problem Limit Theorem Stochastic Differential Equation 
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© Springer-Verlag Berlin Heidelberg 1997

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  • Paul Malliavin

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