Weak ergodicity in non-homogeneous Markov chains
- 1 April 1958
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 54 (2), 233-246
- https://doi.org/10.1017/s0305004100033399
Abstract
The paper deals with weak ergodicity, i.e. the tendency for a chain to ‘forget’ the distant past. This may occur in non-homogeneous chains even if the probabilities of being in a given state do not tend to a limit as the number of trials increases.Investigation of the general conditions of weak ergodicity leads to the definition of a special subclass of regular matrices. Conditions for chains involving regular matrices are also given (§§2,3).Section 4 discusses similarities in asymptotic behaviour between chains whose transition matrices differ only by small amounts.Keywords
This publication has 1 reference indexed in Scilit:
- The ergodic properties of non-homogeneous finite Markov chainsMathematical Proceedings of the Cambridge Philosophical Society, 1956