Summary
This paper presents a detailed probabilistic study of a class of hypoelliptic diffusion processes in ℝ3 including the so-called Brownian motion on the Heisenberg group. We obtain precise estimates for the Green function of the process and the capcity of small compact sets. These estimates are applied to various sample path properties such as the existence of double points or the asymptotic behavior of the volume of a small tubular neighborhood of the path. Differences with the elliptic case are emphasized.
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Dedicated to Klaus Krickeberg on the occasion of his 60th birthday
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Chaleyat-Maurel, M., Le Gall, J.F. Green function, capacity and sample path properties for a class of hypoelliptic diffusion processes. Probability Theory and Related Fields 83, 219–264 (1989). https://doi.org/10.1007/BF00333149
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DOI: https://doi.org/10.1007/BF00333149