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math.PR2022
Explicit fixed points of the smoothing transformation
Jacques Peyrière
We deal with the equation , where the unknown is the distribution of , the variables in the right hand side are inde…
math.PR2014★ 1 cited
Mandelbrot cascades on random weighted trees and nonlinear smoothing transforms
Julien Barral, Jacques Peyrière
We consider complex Mandelbrot multiplicative cascades on a random weigh\-ted tree. Under suitable assumptions, this yields a dynamics $\T$ on laws invariant by random weighted mea…
math.PR2007
Dynamics of Mandelbrot Cascades
Julien Barral, Jacques Peyriere, Zhi-Ying Wen
Mandelbrot multiplicative cascades provide a construction of a dynamical system on a set of probability measures defined by inequalities on moments. To be more specific, beyond the…