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Conditioning an additive functional of a Markov chain to stay nonnegative. I. Survival for a long time

  • Saul D. Jacka (a1), Zorana Lazic (a1) and Jon Warren (a1)

Abstract

Let (X t ) t≥0 be a continuous-time irreducible Markov chain on a finite state space E, let v be a map v: E→ℝ\{0}, and let (φ t ) t≥0 be an additive functional defined by φ t =∫0 t v(X s )d s. We consider the case in which the process (φ t ) t≥0 is oscillating and that in which (φ t ) t≥0 has a negative drift. In each of these cases, we condition the process (X t t ) t≥0 on the event that (φ t ) t≥0 is nonnegative until time T and prove weak convergence of the conditioned process as T→∞.

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Copyright

Corresponding author

Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
∗∗ Email address: s.d.jacka@warwick.ac.uk
∗∗∗ Email address: z.lazic@warwick.ac.uk
∗∗∗∗ Email address: j.warren@warwick.ac.uk

References

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Keywords

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Conditioning an additive functional of a Markov chain to stay nonnegative. I. Survival for a long time

  • Saul D. Jacka (a1), Zorana Lazic (a1) and Jon Warren (a1)

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