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AuthorBelopolskaya, Ya. I. author
TitleStochastic Equations and Differential Geometry [electronic resource] / by Ya. I. Belopolskaya, Yu. L. Dalecky
ImprintDordrecht : Springer Netherlands, 1990
Connect tohttp://dx.doi.org/10.1007/978-94-009-2215-0
Descript XVI, 260 p. online resource

CONTENT

1. Functions and Measures in Linear Spaces -- 1. Spaces, Mappings, Differential Operations -- 2. Measures and Integrals -- 3. Measure Differentiation -- 2. Functions and Measures on Smooth Manifolds -- 1. Smooth Manifolds and Vector Bundles -- 2. Bundle Section, Connections, Differential Operations -- 3. Hilbert and Hilbert-Schmidt Bundles -- 4. Measures on Smooth Manifolds -- 3. Stochastic Equations in Banach Spaces -- 1. Basic Notions -- 2. Stochastic Integrals for Vector and Operator Functions -- 3. Stochastic Equations -- 4. Multiplicative Functionals of Stochastic Processes -- 5. Stochastic Flow -- 4. Stochastic Equations on Smooth Manifolds -- 1. Stochastic Differentials -- 2. Stochastic Differential Equations on Manifolds -- 3. Stochastic Equations in Vector Bundles -- 5. Kolmogorov Equations -- 1. Backward Kolmogorov Equations -- 2. Quasilinear Parabolic Equations -- 3. Forward Kolmogorov Equations -- 6. Diffusion Processes on Lie Groups and Principal Fibre Bundles -- 1. Lie Groups and Smooth Bundles -- 2. Invariant Stochastic Equations -- 3. Stochastic Equations on Manifolds and their Solution Distribution Properties -- Historical Comments -- References


Mathematics Global analysis (Mathematics) Manifolds (Mathematics) Partial differential equations Probabilities Physics Mathematics Probability Theory and Stochastic Processes Partial Differential Equations Global Analysis and Analysis on Manifolds Theoretical Mathematical and Computational Physics



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