  When the output of an atomistic simulation (such as the Gillespie stochastic
simulation algorithm, SSA) can be approximated as a diffusion process, we may
be interested in the dynamic features of the deterministic (drift) component of
this diffusion. We perform traditional scientific computing tasks (integration,
steady state and closed orbit computation, and stability analysis) on such a
drift component using a SSA simulation of the Cyclic Lotka-Volterra system as
our illustrative example. The results of short bursts of appropriately
initialized SSA simulations are used to fit local diffusion models using
Ait-Sahalia's transition density expansions \cite{ait2,aitECO,aitVEC} in a
maximum likelihood framework. These estimates are then coupled with standard
numerical algorithms (such as Newton-Raphson or numerical integration routines)
to help design subsequent SSA experiments. A brief discussion of the validity
of the local diffusion approximation of the SSA simulation (a jump process) is
included.
