Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution

Wojciech Młotkowski; Noriyoshi Sakuma

Banach Center Publications, Tome 95 (2011), p. 271-276 / Harvested from The Polish Digital Mathematics Library

Résumé

We study relations between the Boolean convolution and the symmetrization and the pushforward of order 2. In particular we prove that if μ₁,μ₂ are probability measures on [0,∞) then ${(μ ₁ ⨄ μ ₂)}^{s} = μ ₁^{s} ⨄ μ ₂^{s}$ and if ν₁,ν₂ are symmetric then ${(ν ₁ ⨄ ν ₂)}^{(2)} = ν ₁^{(2)} ⨄ ν ₂^{(2)}$ . Finally we investigate necessary and sufficient conditions under which the latter equality holds.

Publié le : 2011-01-01

Zbl 1259.46056

EUDML-ID : urn:eudml:doc:281922

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     author = {Wojciech M\l otkowski and Noriyoshi Sakuma},
     title = {Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution},
     journal = {Banach Center Publications},
     volume = {95},
     year = {2011},
     pages = {271-276},
     zbl = {1259.46056},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-18}
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Wojciech Młotkowski; Noriyoshi Sakuma. Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution. Banach Center Publications, Tome 95 (2011) pp. 271-276. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-18/