A Course on Rough Paths With an Introduction to Regularity Structures /
Lyons’ rough path analysis has provided new insights in the analysis of stochastic differential equations and stochastic partial differential equations, such as the KPZ equation. This textbook presents the first thorough and easily accessible introduction to rough path analysis. When applied to stoc...
| Main Authors: | , |
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| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2014.
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| Edition: | 1st ed. 2014. |
| Series: | Universitext,
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| Subjects: | |
| Online Access: | https://doi.org/10.1007/978-3-319-08332-2 |
Table of Contents:
- Introduction
- The space of rough paths
- Brownian motion as a rough path
- Integration against rough paths
- Stochastic integration and Itˆo’s formula
- Doob–Meyer type decomposition for rough paths
- Operations on controlled rough paths
- Solutions to rough differential equations
- Stochastic differential equations
- Gaussian rough paths
- Cameron–Martin regularity and applications
- Stochastic partial differential equations
- Introduction to regularity structures
- Operations on modelled distributions
- Application to the KPZ equation.