Operator Exponents of Probability Measures and Lie Semigroups
Jurek, Zbigniew J.
Ann. Probab., Tome 20 (1992) no. 4, p. 1053-1062 / Harvested from Project Euclid
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A notion of $U$-exponents of a probability measure on a linear space is introduced. These are bounded linear operators and it is shown that the set of all $U$-exponents forms a Lie wedge for full measures on finite-dimensional spaces. This allows the construction of $U$-exponents commuting with the symmetry group of a measure in question. Then the set of all commuting exponents is described and elliptically symmetric measures are characterized in terms of their Fourier transforms. Also, self-decomposable measures are identified among those which are operator-self-decomposable. Finally, $S$-exponents of infinitely divisible measures are discussed.
Publié le : 1992-04-14
Classification:  Decomposability semigroup,  tangent space,  wedge,  Lie wedge,  $U$-exponent,  operator-self-decomposable measure,  self-decomposable measure,  Haar measure,  Schur lemma,  60B12,  22A15,  20M20 
@article{1176989817,
     author = {Jurek, Zbigniew J.},
     title = {Operator Exponents of Probability Measures and Lie Semigroups},
     journal = {Ann. Probab.},
     volume = {20},
     number = {4},
     year = {1992},
     pages = { 1053-1062},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176989817}
}

Jurek, Zbigniew J. Operator Exponents of Probability Measures and Lie Semigroups. Ann. Probab., Tome 20 (1992) no. 4, pp.  1053-1062. http://gdmltest.u-ga.fr/item/1176989817/