An introduction to rough paths. (English) Zbl 1041.60051

Azéma, J. (ed.) et al., 37th seminar on probability. Berlin: Springer (ISBN 3-540-20520-9/pbk). Lect. Notes Math. 1832, 1-59 (2003).
This paper aims to be an introduction to T. Lyons’ theory of rough paths, in which integrals of differential forms against irregular paths are defined and differential equations controlled by irregular paths are solved. The theory makes use of iterated integrals of paths, whose algebraic properties are essential. The theory is very well suited for a large number of stochastic processes.
For the entire collection see [Zbl 1027.00025].


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
60H07 Stochastic calculus of variations and the Malliavin calculus
60J57 Multiplicative functionals and Markov processes