The age of a Markov process |
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Authors: | Anthony G Pakes |
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Institution: | Princeton University, U.S.A. |
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Abstract: | The concept of a limiting conditional age distribution of a continuous time Markov process whose state space is the set of non-negative integers and for which {0} is absorbing is defined as the weak limit as t→∞ of the last time before t an associated “return” Markov process exited from {0} conditional on the state, j, of this process at t. It is shown that this limit exists and is non-defective if the return process is ρ-recurrent and satisfies the strong ratio limit property. As a preliminary to the proof of the main results some general results are established on the representation of the ρ-invariant measure and function of a Markov process. The conditions of the main results are shown to be satisfied by the return process constructed from a Markov branching process and by birth and death processes. Finally, a number of limit theorems for the limiting age as j→∞ are given. |
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Keywords: | Markov process ρ-classification Markov branching process limit theorems limiting age strong ratio limit property birth and death process Green function |
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