Rough Volterra equations 1: the algebraic integration setting
نویسندگان
چکیده
We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory called algebraic integration. In the Young case, that is for a driving signal with Hölder exponent γ > 1/2, we obtain a global solution, and are able to handle the case of a singular Volterra coefficient. In case of a driving signal with Hölder exponent 1/3 < γ ≤ 1/2, we get a local existence and uniqueness theorem. The results are easily applied to the fractional Brownian motion with Hurst coefficient H > 1/3.
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