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

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  • Lopusanschi, Olga
  • Simon, Damien

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.

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  • Lopusanschi, Olga & Simon, Damien, 2018. "Lévy area with a drift as a renormalization limit of Markov chains on periodic graphs," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2404-2426.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:7:p:2404-2426
    DOI: 10.1016/j.spa.2017.09.004
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    1. Christian Bayer & Peter K. Friz, 2013. "Cubature on Wiener space: pathwise convergence," Papers 1304.4623, arXiv.org.
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