Singularity spectra of log-normal and log -Poisson stochastic processes. Left: general form of the singularity spectrum D(h), Legendre transform of ξ(q). See text for a definition of D(h), ξ(q), and . Middle and right: singularity spectrum of a log-normal process with d = 2, h_m = 0, and σ_h = 0.5 (middle panel) and of a log-Poisson process with d = 2, D_min = 1.07, and h_min = −0.5 (right panel).