Open Access
April, 1976 A Martingale Approach to Infinite Systems of Interacting Processes
R. A. Holley, D. W. Stroock
Ann. Probab. 4(2): 195-228 (April, 1976). DOI: 10.1214/aop/1176996130


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.


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R. A. Holley. D. W. Stroock. "A Martingale Approach to Infinite Systems of Interacting Processes." Ann. Probab. 4 (2) 195 - 228, April, 1976.


Published: April, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0332.60072
MathSciNet: MR397927
Digital Object Identifier: 10.1214/aop/1176996130

Primary: 60K35
Secondary: 60G45

Keywords: Convergence to equilibrium , Infinite particle system , Martingale problem , Random time change

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 2 • April, 1976
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