Differential Equations Driven by Rough Paths

Ecole d'Eté de Probabilités de Saint-Flour XXXIV-2004
2007
ISBN: 978-3-540-71284-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1908, 116 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 219 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Lyons, Terry J.

Lévy, Thierry

Caruana, Michael J.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

Differential Equations Driven by Moderately Irregular Signals.- The Signature of a Path.- Rough Paths.- Integration Along Rough Paths.- Differential Equations Driven by Rough Paths.