### 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**
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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.