Lévy area with a drift as a renormalization limit of Markov chains on periodic graphs

Résumé

A careful look at rough path topology applied to Brownian motion reveals new possible properties of the well-known Lévy area, in particular the presence of an intrinsic drift of this area. Using renormalization limit of Markov chains on periodic graphs, we present a construction of such a non-trivial drift and give an explicit formula for it. Several examples for which explicit computations are made are included.

Publication
accepted in Stochastic Processes and Applications.
Date
Liens