Stability of infinite systems of stochastic equations

A study is presented of processes with local interaction and infinite systems of Itô equations, which are small perturbations of independent processes at each point of a lattice with noncompact set of values. A survey of results and a complete exposition are devoted to the technique of cluster expansions, which uses estimates of the Lyapunov function type. This technique permits total control over the temporal evolution of the system and, in particular, enables one to prove that the temporal evolution is exponentially convergent.