The Brownian Motion on Aff(R) and Quasi-Local Theorems

Abstract : This paper is concerned with Random walk approximations of the Brownian motion on the Affine group Aff(R). We are in particular interested in the case where the innovations are discrete. In this framework, the return probability of the walk have fractional exponential decay in large time, as opposed to the polynomial one of the continuous object. We prove that integrating those return probabilities on a suitable neighborhood of the origin, the expected polynomial decay is restored. This is what we call a Quasi-local theorem.
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Contributor : Stephane Menozzi <>
Submitted on : Monday, September 18, 2017 - 9:02:24 AM
Last modification on : Wednesday, August 21, 2019 - 10:22:04 AM


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  • HAL Id : hal-01588913, version 1
  • ARXIV : 1709.06411


V Konakov, S Menozzi, Stanislav Molchanov. The Brownian Motion on Aff(R) and Quasi-Local Theorems. 2017. ⟨hal-01588913⟩



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