Ergodicity of Diffusion and Temporal Uniformity of Diffusion Approximation
نویسنده
چکیده
Let {XN(t), t0}, N = 1,2,be a sequence of continuous-parameter Markov processes, and let T,(t)f(x)= EX[f(X,(t))]. Suppose that lim,NcT^(t)f(x)= T(t)f(x), and that convergence is uniform over x and over t E [0, K] for all K < o. When is convergence uniform over t E [0, oo)? Questions of this type are considered under the auxiliary condition that T(t)f(x) converges uniformly over x as t -> oo. 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. DIFFUSION APPROXIMATION; ERGODIC THEORY; GENETIC MODELS
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