Ergodicity of diffusion and temporal uniformity of diffusion approximation
Keyword(s):
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.
1977 ◽
Vol 14
(02)
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pp. 399-404
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Keyword(s):
1982 ◽
Vol 76
(7)
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pp. 3762-3767
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1990 ◽
Vol 146
(21-23)
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pp. 323-333
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1991 ◽
Vol 28
(01)
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pp. 74-83
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Keyword(s):
1959 ◽
Vol 4
(2)
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pp. 198-200
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2004 ◽
Vol 4
(4)
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pp. 1129-1142
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