TY - JOUR

T1 - On the convex hull and winding number of self-similar processes

AU - Davydov, Yu.

N1 - Davydov, Y. On the Convex Hull and Winding Number of Self-Similar Processes. J Math Sci 219, 707–713 (2016). https://doi.org/10.1007/s10958-016-3140-3

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85046863256&partnerID=8YFLogxK

U2 - 10.1007/s10958-016-3140-3

DO - 10.1007/s10958-016-3140-3

M3 - Article

AN - SCOPUS:85046863256

VL - 219

SP - 707

EP - 713

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -