| Summary: | <p style="text-align:justify;"> Rough path analysis can be developed using the concept of controlled paths, and with respect to a topology in which L´evy’s area plays a role. For vectors of irregular paths we investigate the relationship between the property of being controlled and the existence of associated L´evy areas. For two paths, one of which is controlled by the other, a pathwise construction of the L´evy area and therefore of mutual stochastic integrals is possible. If the existence of quadratic variation along a sequence of partitions is guaranteed, this leads us to a study of the pathwise change of variable (Itˆo) formula in the spirit of F¨ollmer, from the perspective of controlled paths. </p>
|
|---|