## An Error Estimate for the Diffusion Approximation in Population Genetics |

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### Contents

THE MARKOV CHAIN AND ITS APPROXIMATION ll | 10 |

DIFFERENTIABILITY PRESERVATION BY | 35 |

DIFFERENTIABILITY PRESERVATION BY | 53 |

3 other sections not shown

### Common terms and phrases

Af(x alleles analogue arbitrary assumed Banach space Bf(x boundary behavior bounded linear operator chapter Ck(Q Ck+l(Q Cl(Q closable in C(Q closed subspace closure Cn contraction semigroup Cn semigroup coefficients compact subsets continuous function contraction semigroup T(t Corollary Define the operators DIFFUSION APPROXIMATION diffusion process discrete semigroup domain P(A estimate l.9 exit boundaries f e C(Q f e P(A Feller finite Fix an integer fundamental solution Furthermore gametes genotype holds uniformly implies infinitesimal Kimura Lemma locus M. F. Norman maps Markov chain Markov Processes Math multi-dimensional multi-index multi-indices mutation na'+b non-negative Norman 37 one-dimensional one-locus polynomials in x,,...,x population genetics positive integer positivity preserving Cn preserving C contraction problem process of Theorem Proposition 4.8 prove R. A. Fisher semigroup on C(Q sequence Stone-Weierstrass Theorem Suppose t)f(q x Theorem l.l thesis tion uniformly in h e weak convergence Wright model x e Q zygote