The Annals of Probability

A Martingale Approach to Infinite Systems of Interacting Processes

R. A. Holley and D. W. Stroock

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996130

Digital Object Identifier
doi:10.1214/aop/1176996130

Mathematical Reviews number (MathSciNet)
MR397927

Zentralblatt MATH identifier
0332.60072

JSTOR
links.jstor.org

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

Keywords
Martingale problem infinite particle system random time change convergence to equilibrium

Citation

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. https://projecteuclid.org/euclid.aop/1176996130


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