  We investigate the Fokker-Planck description of the equal-time statistics of
the three-dimensional Lorenz-63 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.
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.
