A Martingale Approach to Infinite Systems of Interacting Processes

Abstract

Martingale problems associated with the generators of infinite spin flip systems are considered. The stochastic calculus of spin flip systems is developed and applied to the existence and uniqueness questions. Existence of solutions is proved under the assumption that the flip rates are continuous functions of the configurations. Uniqueness theorems are proved under two different conditions and a counterexample to uniqueness in complete generality is given. The techniques also yield ergodic theorems, including rates of convergence, and results concerning mutual absolute continuity of different processes.