Geodesic
Differential independence via an associative product of infinitely many linear functionals
Takahiro Hasebe1
1 Graduate School of Science Kyoto University Kyoto 606-8502, Japan
Colloquium Mathematicum, Tome 124 (2011) no. 1, pp. 79-94

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We generalize the infinitesimal independence appearing in free probability of type B in two directions: to higher order derivatives and other natural independences: tensor, monotone and Boolean. Such generalized infinitesimal independences can be defined by using associative products of infinitely many linear functionals, and therefore the associated cumulants can be defined. These products can be seen as the usual natural products of linear maps with values in formal power series.
DOI : 10.4064/cm124-1-6
Keywords: generalize infinitesimal independence appearing probability type directions higher order derivatives other natural independences tensor monotone boolean generalized infinitesimal independences defined using associative products infinitely many linear functionals therefore associated cumulants defined these products seen usual natural products linear maps values formal power series

Takahiro Hasebe 1

1 Graduate School of Science Kyoto University Kyoto 606-8502, Japan 
@article{10_4064_cm124_1_6,
     author = {Takahiro Hasebe},
     title = {Differential independence via an associative product of infinitely many linear functionals},
     journal = {Colloquium Mathematicum},
     pages = {79--94},
     publisher = {mathdoc},
     volume = {124},
     number = {1},
     year = {2011},
     doi = {10.4064/cm124-1-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm124-1-6/}
}
TY  - JOUR
AU  - Takahiro Hasebe
TI  - Differential independence via an associative product of infinitely many linear functionals
JO  - Colloquium Mathematicum
PY  - 2011
SP  - 79
EP  - 94
VL  - 124
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm124-1-6/
DO  - 10.4064/cm124-1-6
LA  - en
ID  - 10_4064_cm124_1_6
ER  - 
%0 Journal Article
%A Takahiro Hasebe
%T Differential independence via an associative product of infinitely many linear functionals
%J Colloquium Mathematicum
%D 2011
%P 79-94
%V 124
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm124-1-6/
%R 10.4064/cm124-1-6
%G en
%F 10_4064_cm124_1_6
Takahiro Hasebe. Differential independence via an associative product of infinitely many linear functionals. Colloquium Mathematicum, Tome 124 (2011) no. 1, pp. 79-94. doi: 10.4064/cm124-1-6

Cité par Sources :