title: Statistics of the stochastically forced Lorenz attractor by the Fokker-Planck equation and cumulant expansions.
abstract: We investigate the Fokker-Planck description of the equal-time statistics of the three-dimensional Lorenz attractor with additive white noise. The invariant measure is found by computing the zero (or null) mode of the linear Fokker-Planck operator as a problem of sparse linear algebra. Two variants are studied: a self-adjoint construction of the linear operator and the replacement of diffusion with hyperdiffusion. We also access the low-order statistics of the system by a perturbative expansion in equal-time cumulants. A comparison is made to statistics obtained by the standard approach of accumulation via direct numerical simulation. Theoretical and computational aspects of the Fokker-Planck and cumulant expansion methods are discussed.
authors.affiliation: Department of Physics, Box 1843, Brown University, Providence, Rhode Island 02912-1893, USA.
authors.forename: Altan
authors.initials: A
authors.lastname: Allawala
authors.affiliation: Department of Physics, Box 1843, Brown University, Providence, Rhode Island 02912-1893, USA.
authors.forename: J B
authors.initials: JB
authors.lastname: Marston