STOCHASTIC GEOMETRIC ANALYSIS WITH APPLICATIONS

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The book delves into the connections between Stochastic Analysis, Geometry, and Partial Differential Equations (PDEs), emphasizing how geometric structures like Riemannian and sub-Riemannian geometries influence diffusion processes. It explores the implications for solving PDEs and applications in mathematical finance, while unifying these disciplines through the bracket-generating condition, also known as Hörmander's condition. The primary objective is to highlight the shared conditions on vector fields that link PDEs, nonholonomic geometry, and stochastic processes.