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A system is controlled by a control variable. The control variable could be of finite or infinite dimensions. The roughness of control variable has determine the complexity of the system.The control variable could be very rough.

The It\^o functional I is continuous in the topology of uniform convergence in the case of the control variable is one dimensional, Read the rest of this entry »

Fractional calculus is a branch of mathematical analysis that studies the possibility of taking real number powers of the differential operator

$D = \frac{d}{dx} \,$

and the integration operator J. (Usually J is used in favor of I to avoid confusion with other I-like glyphs and identities) Read the rest of this entry »

## Rough paths

This page is dedicated to gather informations on rough paths theory.

bib file of the bibliography below.