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2 (1.1) L 1 axax • +b1(x) 2 iES fES ~ ~ 3 kES ~ ~ ~~ i iES axi J where (ISi)iES are non-negative constants satisfying that supIEsai < + oo, 5i j stands for the Kronecker symbol, and the domain ~D(L) of L is the set of all C2functions defined on X depending on only finitely many coordinates. Let W =C([0, oo)-+X) be the space of all continuous functions w [0, oo) t-cw(t) E X with the topology of uniform convergence on bounded intervals, and let EF (E'2) be the 6-field on W generated by cylinder sets (up to time t). By an (X, L)-diffusion we mean a system {Px, x E X } of probability distributions on (W, EF) that is strongly Markovian and satisfies the following two Conditions : (1.2) Px { w : w(0)= x } =1 for every x E X ,

A certain class of infinite dimensional diffusion processes arising in population genetics