Differential Equations Driven by Rough Paths
Lyons, Terry J.
Differential Equations Driven by Rough Paths École d'Été de Probabilités de Saint-Flour XXXIV - 2004 / [electronic resource] : by Terry J. Lyons, Michael Caruana, Thierry Lévy. - XVIII, 116 p. online resource. - École d'Été de Probabilités de Saint-Flour, 1908 0721-5363 ; . - École d'Été de Probabilités de Saint-Flour, 1908 .
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.
9783540712855
10.1007/978-3-540-71285-5 doi
Global analysis (Mathematics).
Distribution (Probability theory.
Differential Equations.
Analysis.
Probability Theory and Stochastic Processes.
Ordinary Differential Equations.
QA299.6-433
515
Differential Equations Driven by Rough Paths École d'Été de Probabilités de Saint-Flour XXXIV - 2004 / [electronic resource] : by Terry J. Lyons, Michael Caruana, Thierry Lévy. - XVIII, 116 p. online resource. - École d'Été de Probabilités de Saint-Flour, 1908 0721-5363 ; . - École d'Été de Probabilités de Saint-Flour, 1908 .
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.
9783540712855
10.1007/978-3-540-71285-5 doi
Global analysis (Mathematics).
Distribution (Probability theory.
Differential Equations.
Analysis.
Probability Theory and Stochastic Processes.
Ordinary Differential Equations.
QA299.6-433
515