44 citations · 81 across the 4 of their papers we have counts for
4 papers
Yaglom limits can depend on the starting state
R. D. Foley, D. R. McDonald
We construct a simple example, surely known to Harry Kesten, of an R-transient Markov chain on a countable state space S with cemetery state delta. The transition matrix K on S is…
Yaglom limits for R-transient chains with non-trivial Martin boundary
Robert Foley, David McDonald
We give conditions for the existence of a Yaglom limit for R-transient Markov chains with non-trivial rho-Martin entrance boundary (rho=1/R) and we characterize the rho-invariant l…
Bridges and networks: Exact asymptotics
Robert D. Foley, David R. McDonald
We extend the Markov additive methodology developed in [Ann. Appl. Probab. 9 (1999) 110-145, Ann. Appl. Probab. 11 (2001) 596-607] to obtain the sharp asymptotics of the steady sta…
Large deviations of a modified Jackson network: stability and rough asymptotics
Robert D. Foley, David R. McDonald
Consider a modified, stable, two node Jackson network where server 2 helps server 1 when server 2 is idle. The probability of a large deviation of the number of customers at node o…