Abstract
This article aims to be an introduction to the theory of rough paths, in which integrals of differential forms against irregular paths and differential equations controlled by irregular paths are defined. This theory makes use of an extension of the notion of iterated integrals of the paths, whose algebraic properties appear to be fundamental. This theory is well-suited for stochastic processes.
Keywords: controlled differential equations, integration against irregular paths, p-variation, stochastic processes, iterated integrals, Chen series, geometric multiplicative functional
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lejay, A. (2003). An Introduction to Rough Paths. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVII. Lecture Notes in Mathematics, vol 1832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40004-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-40004-2_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20520-3
Online ISBN: 978-3-540-40004-2
eBook Packages: Springer Book Archive