Elliptic Estimates Through Stochastic Analysis
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.
KeywordsVector Field Stochastic Differential Equation Stochastic Analysis Stochastic Calculus Transfer Principle
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