Controlled differential equations as Young integrals: a simple approach
- Lejay, Antoine
Publication date
January 2010
DOI Publisher
Elsevier BV ISSN
0022-0396 Citation count (estimate)
22Abstract
International audienceThe theory of rough paths allows one to define controlled differential equations driven by a path which is irregular. The most simple case is the one where the driving path has finite p-variations with 1≤ p <2, in which case the integrals are interpreted as Young integrals. The prototypal example is given by Stochastic Differential Equations driven by fractional Brownian motion with Hurst index greater than 1/2. Using simple computations, we give the main results regarding this theory --- existence, uniqueness, convergence of the Euler scheme, flow property, ... --- which are spread out among several articles
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