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Differential Equations Driven by Rough Paths [electronic resource] :École d'Été de Probabilités de Saint-Flour XXXIV - 2004 / by Terry J. Lyons, Michael Caruana, Thierry Lévy.

by Lyons, Terry J [author.]; Caruana, Michael [author.]; Lévy, Thierry [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Mathematics: 1908Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.Description: XVIII, 109 p. 3 illus. online resource.ISBN: 9783540712855.Subject(s): Mathematics | Differential Equations | Distribution (Probability theory) | Mathematics | Probability Theory and Stochastic Processes | Ordinary Differential EquationsDDC classification: 519.2 Online resources: Click here to access online
Contents:
Differential Equations Driven by Moderately Irregular Signals -- The Signature of a Path -- Rough Paths -- Integration Along Rough Paths -- Differential Equations Driven by Rough Paths.
In: Springer eBooksSummary: 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.
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Differential Equations Driven by Moderately Irregular Signals -- The Signature of a Path -- Rough Paths -- Integration Along Rough Paths -- Differential Equations Driven by Rough Paths.

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.

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