With operator truncation and constant coefficients, Is the discretization Toeplitz?

[jlperla]

It seems like the discretized operator is Toeplitz as long as (1) the parameters don't change as a function of $z$; (2) the boundary conditions are `truncated' as opposed to directly putting in the reflecting barrier; and (3) grid spacing is uniform.

The truncation of the operator seems to be used in https://ecommons.cornell.edu/handle/1813/5453 and it is worth seeing if the solution is close enough. This would be unlikely to work for the stationary distribution, though.

If so, then Toeplitz solvers could be used for the sparse stationary system, and possibly even the time-varying system.