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

Olga Lopusanschi and Damien Simon

Stochastic Processes and their Applications, 2018, vol. 128, issue 7, 2404-2426

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 with explicit computations are included.

Date: 2018
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DOI: 10.1016/j.spa.2017.09.004

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