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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 »

Rough paths

 

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

bib file of the bibliography below.

 

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The following articles are about Rough path theory which is developed by T. Lyons from Oxford University:

  1.  Lyons-Victoir extension
  2. An introduction to Rough paths

For more reference on Rough paths, one could visit Rough paths.