Conditioning an Additive Functional of a Markov Chain to Stay Non-negative I:survival for a Long Time
نویسندگان
چکیده
Let (Xt)t≥0 be a continuous-time irreducible Markov chain on a finite statespace E, let v be a map v : E → R\{0} and let (φt)t≥0 be an additive functional defined by φt = ∫ t 0 v(Xs)ds. We consider the cases where the process (φt)t≥0 is oscillating and where (φt)t≥0 has a negative drift. In each of the cases we condition the process (Xt, φt)t≥0 on the event that (φt)t≥0 stays non-negative until time T and prove weak convergence of the conditioned process as T →∞.
منابع مشابه
Conditioning an Additive Functional of a Markov Chain to Stay Non-negative Ii: Hitting a High Level
Let (Xt)t≥0 be a continuous-time irreducible Markov chain on a finite statespace E, let v : E → R\{0} and let (φt)t≥0 be defined by φt = ∫ t 0 v(Xs)ds. We consider the cases where the process (φt)t≥0 is oscillating and where (φt)t≥0 has a negative drift. In each of the cases we condition the process (Xt, φt)t≥0 on the event that (φt)t≥0 hits level y before hitting zero and prove weak convergenc...
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