On Markov chains with an enumerable infinity of states
- 24 October 1952
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 48 (4) , 587-591
- https://doi.org/10.1017/s0305004100076362
Abstract
Consider the infinite system of linear ‘inequations’, in which the coefficients pij have the two properties We define as properly divergent (p.d.) a solution, {xi} (i = 0, 1, 2, …), such that and such that |xi| < ∞ for i < ∞. Since {k + xi} is also a solution for any non-negative constant k, there is no loss in generality in assuming (as we always shall) in place of this last condition that We are concerned with conditions for the existence of p.d. solutions.This publication has 2 references indexed in Scilit:
- On non-dissipative Markoff chains with an enumerable infinity of statesMathematical Proceedings of the Cambridge Philosophical Society, 1951
- Markoff chains with an enumerable number of states and a class of cascade processesMathematical Proceedings of the Cambridge Philosophical Society, 1951