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This book aims to provide a self-contained introduction to the local geometry of the stochastic flows. It studies the hypoelliptic operators, which are written in Hörmander's form, by using the connection between stochastic flows and partial differential equations. The book stresses the author's view that the local geometry of any stochastic flow is determined very precisely and explicitly by a universal formula referred to as the Chen-Strichartz formula. The natural geometry associated with the Chen-Strichartz formula is the sub-Riemannian geometry, and its main tools are introduced throughou

Stochastic geometry. --- Flows (Differentiable dynamical systems) --- Stochastic differential equations. --- Differentiable dynamical systems --- Differential equations --- Fokker-Planck equation --- Geometry --- Equations différentielles stochastiques --- Géométrie stochastique

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Random differential equations in science and engineering

BEquations diffberentielles stochastiques. --- Stochastic differential equations. --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- Differential equations. --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- 517.91 Differential equations --- Differential equations --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Stochastic differential equations --- Equations différentielles stochastiques --- ELSEVIER-B EPUB-LIV-FT --- Équations différentielles stochastiques.