Bilateral Canonical Cascades: Multiplicative Refinement Paths to Wiener's and Variant Fractional Brownian Limits

Julien Barral, Benoit Mandelbrot

The original density is 1 for $t\in (0,1)$, $b$ is an integer base ($b\ge 2$%), and $p\in (0,1)$ is a parameter. The first construction stage divides the unit interval into $b$ su…