The Annals of Probability

A Martingale Approach to Infinite Systems of Interacting Processes

R. A. Holley and D. W. Stroock

Full-text: Open access


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.

Article information

Ann. Probab., Volume 4, Number 2 (1976), 195-228.

First available in Project Euclid: 19 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60G45

Martingale problem infinite particle system random time change convergence to equilibrium


Holley, R. A.; Stroock, D. W. A Martingale Approach to Infinite Systems of Interacting Processes. Ann. Probab. 4 (1976), no. 2, 195--228. doi:10.1214/aop/1176996130.

Export citation