A study of non-linear autoregressive processes: Differential theory

Summary It is shown how the general analytical expression of an autoregression, whose stationary solution has an arbitrary given form, can be obtained. The central-limit theorem is used to state a correspondence between autoregression and relevant diffusion equation which not only permits to give analytical form to the stationary distribution of a given autoregression, but also to obtain appropriate series expansions of its fundamental solution and the exact relaxation constants. The interest of the analysis in the context of Monte Carlo simulations of relaxation and steady-state processes is discussed. The procedure is illustrated by two examples of interest in the field of ionized gases.