Differential Equations Driven by Rough Paths
Ecole d’Eté de Probabilités de Saint-Flour XXXIV-2004
Authors: Lyons, Terry J., Caruana, Michael J., Lévy, Thierry
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- About this book
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Each year young mathematicians congregate in Saint Flour, France, and listen to extended lecture courses on new topics in Probability Theory.
The goal of these notes, representing a course given by Terry Lyons in 2004, is to provide a straightforward and self supporting but minimalist account of the key results forming the foundation of the theory of rough paths. The proofs are similar to those in the existing literature, but have been refined with the benefit of hindsight. The theory of rough paths aims to create the appropriate mathematical framework for expressing the relationships between evolving systems, by extending classical calculus to the natural models for noisy evolving systems, which are often far from differentiable.
- Reviews
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From the reviews:
"The present book is based on lectures delivered by Lyons at the Saint-Flour Summer School in July 2004. … It is primarily intended for a reader who has never been exposed to the theory of rough paths … . There is no doubt that the book will be useful to anyone trying to enter the sophisticated ground of rough path theory–students as well as experienced researchers." (Bohdan Maslowski, Mathematical Reviews, Issue 2009 c)
“The book provides an introduction to and a survey of the key concepts and results of the theory of rough paths. It grew out of the lecture notes for the corresponding lectures given at the Ecole d’Eté de Probabilités de Saint-Flour XXXIV – 2004. … The book is very well readable and will be useful for everyone interested in learning about the theory of rough paths.” (Evelyn Buckwar, Zentralblatt MATH, Vol. 1176, 2010)
- Table of contents (5 chapters)
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Differential Equations Driven by Moderately Irregular Signals
Pages 1-24
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The Signature of a Path
Pages 25-40
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Rough Paths
Pages 41-61
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Integration Along Rough Paths
Pages 63-79
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Differential Equations Driven by Rough Paths
Pages 81-93
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Table of contents (5 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Differential Equations Driven by Rough Paths
- Book Subtitle
- Ecole d’Eté de Probabilités de Saint-Flour XXXIV-2004
- Authors
-
- Terry J. Lyons
- Michael J. Caruana
- Thierry Lévy
- Series Title
- École d'Été de Probabilités de Saint-Flour
- Series Volume
- 1908
- Copyright
- 2007
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-540-71285-5
- DOI
- 10.1007/978-3-540-71285-5
- Softcover ISBN
- 978-3-540-71284-8
- Series ISSN
- 0721-5363
- Edition Number
- 1
- Number of Pages
- XVIII, 116
- Topics
