Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions
Bertoin, Jean ; Roynette, Bernard ; Yor, Marc
HAL, hal-00003605 / Harvested from HAL
Text on HAL
We describe some connections, via composition, between two functional spaces: the space of (sub)critical branching mechanisms and the space of Bernstein functions. The functions ${\bf e}_\alpha: x\to x^{\alpha}$ where $x\geq0$ and $0<\alpha\leq 1/2$, and in particular the critical parameter $\alpha=1/2$, play a distinguished role.
Publié le : 2004-12-16
Classification:  stable process,  Bernstein function,  branching mechanism,  subordination,  MSC 60E07,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-00003605,
     author = {Bertoin, Jean and Roynette, Bernard and Yor, Marc},
     title = {Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00003605}
}

Bertoin, Jean; Roynette, Bernard; Yor, Marc. Some Connections Between (Sub)Critical Branching Mechanisms and Bernstein Functions. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00003605/