In:
Probability in the Engineering and Informational Sciences, Cambridge University Press (CUP), Vol. 8, No. 1 ( 1994-01), p. 1-19
Abstract:
We consider time-inhomogeneous Markov chains on a finite state-space, whose transition probabilities p ij ( t ) = c ij ε( t ) V ij are proportional to powers of a vanishing small parameter ε( t ). We determine the precise relationship between this chain and the corresponding time-homogeneous chains p ij = c ij ε( t ) v ij , as ε ↘ 0. Let { } be the steady-state distribution of this time-homogeneous chain. We characterize the orders { η ι } in = θ(ε ηι ). We show that if ε( t ) ↘ 0 slowly enough, then the timewise occupation measures β ι := sup { q 〉 0 | Prob(x( t ) = i) = + ∞}, called the recurrence orders, satisfy β i — β j = η j — η i . Moreover, : = { η ι | η ι = min j } is the set of ground states of the time-homogeneous chain, then x(t) → . in an appropriate sense, whenever η( t ) is “cooled” slowly. We also show that there exists a critical ρ * such that x(t) → if and only if = + ∞. We characterize this critical rate as ρ * = max .min min max . Finally, we provide a graph algorithm for determining the orders [η i ] [β i ] and the critical rate ρ *.
Type of Medium:
Online Resource
ISSN:
0269-9648
,
1469-8951
DOI:
10.1017/S0269964800003168
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1994
detail.hit.zdb_id:
2010880-1
SSG:
24,1
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