Rough Volterra equations 1: the algebraic integration setting

Details Rough Volterra equations 1: the algebraic integration setting Rough Volterra equations 1: the algebraic integration setting

2008-09-11

arxiv.org/abs/0809.2000v1

Mathematics

Probability

31 pages

Scientific paper

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 H\"older exponent greater than 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 H\"older exponent in (1/3,1/2], 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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