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Paper No. 05-4

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SD Jacka, Z Lazic and J Warren

Conditioning an Additive Functional of a Markov Chain to stay Non-Negative I: Survival For a Long Time

Date: May 2005

Abstract: Let X be a continuous-time irreducible Markov chain on a finite statespace E, and let ϕ be an additive functional of X. We consider the cases where the process ϕ is oscillating and where ϕ has a negative drift. In each of these cases we condition the process X on the event that ϕ stays non-negative until time T, and prove weak convergence of the conditioned process as T tends to ∞.