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Remarks on random countable stable zonotopes. / Davydov, Youri; Paulauskas, Vygantas.

In: Statistics and Probability Letters, Vol. 153, 10.2019, p. 187-191.

Research output: Contribution to journal › Article › peer-review

Harvard

Davydov, Y & Paulauskas, V 2019, 'Remarks on random countable stable zonotopes', Statistics and Probability Letters, vol. 153, pp. 187-191. https://doi.org/10.1016/j.spl.2019.06.018

APA

Davydov, Y., & Paulauskas, V. (2019). Remarks on random countable stable zonotopes. Statistics and Probability Letters, 153, 187-191. https://doi.org/10.1016/j.spl.2019.06.018

Vancouver

Davydov Y, Paulauskas V. Remarks on random countable stable zonotopes. Statistics and Probability Letters. 2019 Oct;153:187-191. https://doi.org/10.1016/j.spl.2019.06.018

Author

Davydov, Youri ; Paulauskas, Vygantas. / Remarks on random countable stable zonotopes. In: Statistics and Probability Letters. 2019 ; Vol. 153. pp. 187-191.

BibTeX

@article{a220b23d65194b7e8188d93e37ee9e9a,
title = "Remarks on random countable stable zonotopes",
abstract = "In the paper we study random stable countable zonotopes in Rd, given by [Formula presented], where ⊕ stands for Minkowski sum, Γk=∑1 kτj, {τj,j≥1} are i.i.d. random variables with common standard exponential distribution, and {εk,k≥1} are i.i.d. random vectors in Rd with common distribution σ, concentrated on the unit sphere of Rd. The sequences (τk) and (εk) are supposed to be independent. We consider these random sets as elements of the space Kd of all compact convex subsets of Rd with the Hausdorff distance. The boundary of Zα has non-trivial Cantor-type structure, and, in the case d=2 and under mild condition on σ, we prove that the Hausdorff dimension of the set of extremal points of the boundary of Zα is equal to α. As a by-product we provide some kind of geometrical characterization of (non-random) countable zonotopes in the class of zonoids, which are limits of zonotopes.",
keywords = "Countable random zonotopes, Hausdorff dimension, Zonoids, Zonotopes, SETS",
author = "Youri Davydov and Vygantas Paulauskas",
year = "2019",
month = oct,
doi = "10.1016/j.spl.2019.06.018",
language = "English",
volume = "153",
pages = "187--191",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Remarks on random countable stable zonotopes

AU - Davydov, Youri

AU - Paulauskas, Vygantas

PY - 2019/10

Y1 - 2019/10

N2 - In the paper we study random stable countable zonotopes in Rd, given by [Formula presented], where ⊕ stands for Minkowski sum, Γk=∑1 kτj, {τj,j≥1} are i.i.d. random variables with common standard exponential distribution, and {εk,k≥1} are i.i.d. random vectors in Rd with common distribution σ, concentrated on the unit sphere of Rd. The sequences (τk) and (εk) are supposed to be independent. We consider these random sets as elements of the space Kd of all compact convex subsets of Rd with the Hausdorff distance. The boundary of Zα has non-trivial Cantor-type structure, and, in the case d=2 and under mild condition on σ, we prove that the Hausdorff dimension of the set of extremal points of the boundary of Zα is equal to α. As a by-product we provide some kind of geometrical characterization of (non-random) countable zonotopes in the class of zonoids, which are limits of zonotopes.

AB - In the paper we study random stable countable zonotopes in Rd, given by [Formula presented], where ⊕ stands for Minkowski sum, Γk=∑1 kτj, {τj,j≥1} are i.i.d. random variables with common standard exponential distribution, and {εk,k≥1} are i.i.d. random vectors in Rd with common distribution σ, concentrated on the unit sphere of Rd. The sequences (τk) and (εk) are supposed to be independent. We consider these random sets as elements of the space Kd of all compact convex subsets of Rd with the Hausdorff distance. The boundary of Zα has non-trivial Cantor-type structure, and, in the case d=2 and under mild condition on σ, we prove that the Hausdorff dimension of the set of extremal points of the boundary of Zα is equal to α. As a by-product we provide some kind of geometrical characterization of (non-random) countable zonotopes in the class of zonoids, which are limits of zonotopes.

KW - Countable random zonotopes

KW - Hausdorff dimension

KW - Zonoids

KW - Zonotopes

KW - SETS

UR - http://www.scopus.com/inward/record.url?scp=85068145349&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/remarks-random-countable-stable-zonotopes

U2 - 10.1016/j.spl.2019.06.018

DO - 10.1016/j.spl.2019.06.018

M3 - Article

AN - SCOPUS:85068145349

VL - 153

SP - 187

EP - 191

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -

ID: 49897516