在球体上投掷球

摘要：

在欧几里得空间上抛球已经被考虑了一段时间。通过适当的重整化，得到了分数阶布朗运动作为极限对象。在本文中，我们研究球投掷领域。表现出不同的行为：我们仍然得到高斯极限，但不再是分数布朗运动。然而，当自相似性指数$H$小于小于1/2时，极限是局部自相似的。

英文摘要：

Ball throwing on Euclidean spaces has been considered for a while. A suitable renormalization leads to a fractional Brownian motion as limit object. In this paper we investigate ball throwing on spheres. A different behavior is exhibited: we still get a Gaussian limit but which is no longer a fractional Brownian motion. However the limit is locally self-similar when the self-similarity index $H$ is less than 1/2.

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