  We address the problem of Lyapunov function construction for a class of
continuous-time Markov chains with affine transition rates, typically
encountered in stochastic chemical kinetics. Following an optimization
approach, we take advantage of existing bounds from the Foster-Lyapunov
stability theory to obtain functions that enable us to estimate the region of
high stationary probability, as well as provide upper bounds on moments of the
chain. Our method can be used to study the stationary behavior of a given chain
without resorting to stochastic simulation, in a fast and efficient manner.
