Multiscale sparse microcanonical models2018
We study approximations of non-Gaussian stationary processes having long range correlations with microcanonical models. These models are conditioned by the empirical value of an energy vector, evaluated on a single realization. Asymptotic properties of maximum entropy microcanonical and macrocanonical processes and their convergence to Gibbs measures are reviewed. We show that the Jacobian of the energy vector controls the entropy rate of microcanonical processes.