Abstract
Let {XN(t), t ≧ 0}, N = 1, 2, … be a sequence of continuous-parameter Markov processes, and let TN(t)f(x) = Ex[f(XN(t))]. Suppose that limN→∞TN(t)f(x)= T(t)f(x), and that convergence is uniform over x and over t ∈ [0, K] for all K < ∞. When is convergence uniform over t ∈ [0, ∞)? Questions of this type are considered under the auxiliary condition that T(t)f(x) converges uniformly over x as t → ∞. A criterion for such ergodicity is given for semigroups T(t) associated with one-dimensional diffusions. The theory is illustrated by applications to genetic models.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference8 articles.
1. Extensions of Trotter's operator semigroup approximation theorems
2. Some properties of one-dimensional diffusion processes;Maruyama;Mem. Fac. Sci. Kyushu Univ. Ser. A,1957
Cited by
14 articles.
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