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

O. Lopusanschi, D. Simon,

Stochastic Processes and their Applications, 128, July 2018, Pages 2404-2426 ,

https://arxiv.org/abs/1604.08947,

Abstract:

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.