Open Access
December, 1978 Controlled Spin-Flip Systems
Lawrence Gray
Ann. Probab. 6(6): 953-974 (December, 1978). DOI: 10.1214/aop/1176995386


We introduce a new tool into the study of spin-flip processes, which we call controlled spin-flip systems. For each spin-flip process we define a related class of controlled spin-flip systems. Our main theorem states that bounds on the behavior of a spin-flip process can be obtained by studying the behavior of the related controlled spin-flip system. Since controlled spin-flip systems are in general easier to work with than regular spin-flip processes (they correspond to finite state space Markov processes), our main theorem has applications to some of the important problems concerning spin-flip processes. In particular, we discuss several applications to the uniqueness problem. These include proofs of some new results, as well as new proofs of earlier results.


Download Citation

Lawrence Gray. "Controlled Spin-Flip Systems." Ann. Probab. 6 (6) 953 - 974, December, 1978.


Published: December, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0392.60084
MathSciNet: MR512413
Digital Object Identifier: 10.1214/aop/1176995386

Primary: 60K35

Keywords: controlled spin-flip systems , Martingale problem , Spin-flip process

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 6 • December, 1978
Back to Top