ON THE DIFFUSION OPERATOR IN POPULATION GENETICS†

Abstract. W.Choi([1]) obtains a complete description of ergodic prop-erty and several property by making use of the semigroup method. In this note, we shall consider separately the martingale problems for two opera-tors A and B as a detail decomposition of operator L. A key point is that the (K;L; p)-martingale problem in population genetics model is related to diffusion processes, so we begin with some a priori estimates and we shall show existence of contraction semigroup fTtg associated with decomposi-tion operator A. AMS Mathematics Subject Classification: 92D10, 60H30, 60G44. Key words and phrases: diffusion operator, martingale problem, contrac