论文标题
布朗运动和布朗床单的路径规律性
Path regularity of Brownian motion and Brownian sheet
论文作者
论文摘要
通过P.Lévy的工作，已知Brownian运动的样本路径几乎可以满足某些Hölder规律性条件。后来，Ciesielski改进了这种情况，他研究了BESOV和BESOV-ORLICZ空间的这些路径的规律性。我们审查了这些结果，并提出了BESOV类型的新功能空间，严格比Ciesielski和Lévy的功能小，Brownian运动的样本路径几乎肯定位于那里。本着同样的精神，我们审查并扩展了Kamont的工作，Kamont的工作调查了多元布朗纸和主导混合平滑度的功能空间相同的问题。
By the work of P. Lévy, the sample paths of the Brownian motion are known to satisfy a certain Hölder regularity condition almost surely. This was later improved by Ciesielski, who studied the regularity of these paths in Besov and Besov-Orlicz spaces. We review these results and propose new function spaces of Besov type, strictly smaller than those of Ciesielski and Lévy, where the sample paths of the Brownian motion lie in almost surely. In the same spirit, we review and extend the work of Kamont, who investigated the same question for the multivariate Brownian sheet and function spaces of dominating mixed smoothness.
