Mathematics – Dynamical Systems
Scientific paper
2011-12-19
Mathematics
Dynamical Systems
15 pages
Scientific paper
In this paper we show that any one-dimensional stationary, finite-valued Markov Random Field (MRF) is a Markov chain, without any mixing condition or condition on the support. Our proof makes use of two properties of the support $X$ of a finite-valued stationary MRF: 1) $X$ is non-wandering (this is a property of the support of any finite-valued stationary process) and 2) $X$ is a topological Markov field (TMF). The latter is a new property that sits in between the classes of shifts of finite type and sofic shifts, which are well-known objects of study in symbolic dynamics. Here, we develop the TMF property in one dimension, and we will develop this property in higher dimensions in a future paper. While we are mainly interested in discrete-time finite-valued stationary MRF's, we also consider continuous-time, finite-valued stationary MRF's, and show that these are (continuous-time) Markov chains as well.
Chandgotia Nishant
Han Guangyue
Marcus Brian
Meyerovitch Tom
Pavlov Ronnie
No associations
LandOfFree
One dimensional Markov random fields, Markov chains and Topological Markov fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with One dimensional Markov random fields, Markov chains and Topological Markov fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and One dimensional Markov random fields, Markov chains and Topological Markov fields will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-210124