  We derive fractional Brownian motion and stochastic processes with
multifractal properties using a framework of network of Gaussian conditional
probabilities. This leads to the derivation of new representations of
fractional Brownian motion. These constructions are inspired from
renormalization. The main result of this paper consists of constructing each
increment of the process from two-dimensional gaussian noise inside the
light-cone of each seperate increment. Not only does this allows us to derive
fractional Brownian motion, we can introduce extensions with multifractal
flavour. In another part of this paper, we discuss the use of the multi-scale
entanglement renormalization ansatz (MERA), introduced in the study critical
systems in quantum spin lattices, as a method for sampling integrals with
respect to such multifractal processes. After proper calibration, a MERA
promises the generation of a sample of size $N$ of a multifractal process in
the order of $O(N\log(N))$, an improvement over the known methods, such as the
Cholesky decomposition and the circulant methods, which scale between $O(N^2)$
and $O(N^3)$.
