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Delay equations driven by rough paths. (English) Zbl 1190.60046
Summary: We illustrate the flexibility of the algebraic integration formalism introduced in [M. Gubinelli, J. Funct. Anal. 216, No. 1, 86–140 (2004; Zbl 1058.60037)], by establishing an existence and uniqueness result for delay equations driven by rough paths. We then apply our results to the case where the driving path is a fractional Brownian motion with Hurst parameter $$H>1/3$$.

##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60H05 Stochastic integrals 60H07 Stochastic calculus of variations and the Malliavin calculus 60G15 Gaussian processes
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