Controlled differential equations as Young integrals: A simple approach
- Lejay, Antoine
DOIAbstract
AbstractThe 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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