Stochastic Equations and Differential Geometry
Main Authors: | , |
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Format: | eBook |
Language: | English |
Published: |
Dordrecht
Springer Netherlands
1990, 1990
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Edition: | 1st ed. 1990 |
Series: | Mathematics and its Applications, Soviet Series
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Subjects: | |
Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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