Nested classes of $C$-decomposable laws
Bunge, John
Ann. Probab., Tome 25 (1997) no. 4, p. 215-229 / Harvested from Project Euclid
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A random variable $X$ is C-decomposable if $X =_D cX + Y_c$ for all $c$ in $C$, where $_c$ is a random variable independent of $X$ and $C$ is a closed multiplicative subsemigroup of [0, 1]. $X$ is self-decomposable if $C = [0, 1]$ . Extending an idea of Urbanik in the self-decomposable case, we define a decreasing sequence of subclasses of the class of $C$-decomposable laws, for any $C$. We give a structural representation for laws in these classes, and we show that laws in the limiting subclass are infinitely divisible. We also construct noninfinitely divisible examples, some of which are continuous singular.
Publié le : 1997-01-14
Classification:  Class $L$ distribution,  decomposability semigroup,  infinite Bernoulli convolution,  infinitely divisible measure,  normed sum,  self-decomposable measure,  60E05,  60F05 
@article{1024404286,
     author = {Bunge, John},
     title = {Nested classes of $C$-decomposable laws},
     journal = {Ann. Probab.},
     volume = {25},
     number = {4},
     year = {1997},
     pages = { 215-229},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1024404286}
}

Bunge, John. Nested classes of $C$-decomposable laws. Ann. Probab., Tome 25 (1997) no. 4, pp.  215-229. http://gdmltest.u-ga.fr/item/1024404286/