L\'evy area with a drift as a renormalization limit of Markov chains on periodic graphs

Olga Lopusanschi; Damien Simon

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arXiv · 1604.08947

L\'evy area with a drift as a renormalization limit of Markov chains on periodic graphs

Olga Lopusanschi·Damien Simon

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Abstract

A careful look at rough path topology applied to Brownian motion reveals new possible properties of the well-known L\'evy 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.

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Olga Lopusanschi, Damien Simon. 2016-04-29. L\'evy area with a drift as a renormalization limit of Markov chains on periodic graphs. https://arxiv.org/abs/1604.08947

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