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- Title
VIRTUAL MARKOV CHAINS.
- Authors
EVANS, STEVEN N.; JAFFE, ADAM Q.
- Abstract
We introduce the space of virtual Markov chains (VMCs) as a pro-jective limit of the spaces of all finite state space Markov chains (MCs), in the same way that the space of virtual permutations is the projective limit of the spaces of all permutations of finite sets. We introduce the notions of virtual initial distribution (VID) and a virtual transition matrix (VTM), and we show that the law of any VMC is uniquely characterized by a pair of a VID and VTM which have to satisfy a certain compatibility condition. Lastly, we study various properties of compact convex sets associated to the theory of VMCs, including that the Birkhoff-von Neumann theorem fails in the virtual setting.
- Subjects
VON Neumann, John, 1903-1957; MARKOV processes; CONVEX sets; SET theory; PROJECTIVE spaces; PERMUTATIONS
- Publication
New Zealand Journal of Mathematics, 2021, Vol 52, p511
- ISSN
1171-6096
- Publication type
Article
- DOI
10.53733/147