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Stochastic processes --- Stochastic analysis. --- Stochastic differential equations. --- Analyse stochastique --- Equations différentielles stochastiques --- Stochastic analysis --- Flows (Differentiable dynamical systems) --- Stochastic differential equations --- Equations différentielles stochastiques

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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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"In this memoir, we show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation"--

Fluid dynamics --- Inviscid flow. --- Flows (Differentiable dynamical systems) --- Fluid mechanics. --- Smoothness of functions. --- Geostrophic currents --- Interval analysis (Mathematics) --- Differential equations, Nonlinear --- Mathematical models. --- Numerical solutions.

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Operator theory --- Differentiable dynamical systems --- Flows (Differentiable dynamical systems) --- Hyperbolic spaces --- Invariant manifolds --- Invariants --- Manifolds (Mathematics) --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Differentiable dynamical systems. --- Systèmes dynamiques. --- Hyperbolic spaces. --- Espaces hyperboliques. --- Invariant manifolds. --- Variétés invariantes. --- Flows (Differentiable dynamical systems).

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Topology --- Flows (Differentiable dynamical systems) --- Topological dynamics. --- Intersection theory (Mathematics) --- Flots (dynamique différentiable) --- Dynamique topologique. --- Intersections, Théorie des. --- Intersection theory --- Topological dynamics --- Dynamics, Topological --- Differentiable dynamical systems --- Geometry, Algebraic