Consider the linear nonhomogeneous fixed-point equation R=D∑i=1NCiRi+Q, where (Q,N,C1,C2,…) is a random vector with N∈{0,1,2,3,…}∪{∞},Ci≥0 for all i∈N, P(|Q|0)0, and {Ri}i∈N is a sequence of i.i.d. random variables independent of (Q,N,C1,C2,…) having the same distribution as...

Multifractal random walks (MRW) correspond to simple solvable “stochastic volatility” processes. Moreover, they provide a simple interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that they are able to...