Title: An iterative aggregation and disaggregation approach to the calculation of steady-state distributions of continuous processes,
Abstract: A mapping of the process on a continuous configuration space to the symbolic
representation of the motion on a discrete state space will be combined with an
iterative aggregation and disaggregation (IAD) procedure to obtain steady state
distributions of the process. The IAD speeds up the convergence to the unit
eigenvector, which is the steady state distribution, by forming smaller
aggregated matrices whose unit eigenvector solutions are used to refine
approximations of the steady state vector until convergence is reached. This
method works very efficiently and can be used together with distributed or
parallel computing methods to obtain high resolution images of the steady state
distribution of complex atomistic or energy landscape type problems. The method
is illustrated in two numerical examples. In the first example the transition
matrix is assumed to be known. The second example represents an overdamped
Brownian motion process subject to a dichotomously changing external potential.