From Ordinary Differential Equations to Stochastic Flow: The Transfer Principle
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.
KeywordsOrdinary Differential Equation Vector Field Cauchy Problem Limit Theorem Stochastic Differential Equation
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