On the Convex Hull and Winding Number of Self-Similar Processes
- Authors: Davydov Y.1
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Affiliations:
- University Lille 1, CNRS
- Issue: Vol 219, No 5 (2016)
- Pages: 707-713
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/238658
- DOI: https://doi.org/10.1007/s10958-016-3140-3
- ID: 238658
Cite item
Abstract
It is well known that for a standard Brownian motion (BM) {B(t), t ≥ 0} with values in Rd, its convex hull V (t) = conv{B(s), s ≤ t} with probability 1 for each t > 0 contains 0 as an interior point. We also know that the winding number of a typical path of a two-dimensional BM is equal to +∞. The aim of this paper is to show that these properties are not specifically “Brownian,” but hold for a much larger class of d-dimensional self-similar processes. This class contains, in particular, d-dimensional fractional Brownian motions and (concerning convex hulls) strictly stable Lévy processes. Bibliography: 10 titles.
About the authors
Yu. Davydov
University Lille 1, CNRS
Author for correspondence.
Email: youri.davydov@univ-lille1.fr
France, Lille