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Consider a time-continuous nonhomogeneous Markovian stochastic process V having state space A⁰. Let A \ A⁰ and let P₀₈₉ (\, t) be the i \ j transition probability of the Markovian stochastic process VA arising in the hypothetical situation where states A⁰ - A have been eliminated from the state space of V. Based upon the concept of Kaplan and Meier's product-limit estimator, a nonparametric estimator ₀₈₉ (\, t) is formulated which is proved to be uniformly strongly consistent and asymptotically unbiased. These results generalize those by Aalen for the special case in which A⁰ has one transient state.
Thomas R. Fleming (Fri,) studied this question.