# THE APPLICATION OF STOCHASTIC ANALYSIS TO COUNTABLE ALLELIC DIFFUSION MODEL

• Choi, Won (Department of Mathematics, University of Incheon)
• Published : 2004.05.01

#### Abstract

In allelic model X = ($\chi_1\chi$_2ㆍㆍㆍ, \chi_d$), M_f(t) = f(p(t)) -${{\int^t}_0}\;Lf(p(t))ds\$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show existence and uniqueness of solution for stochastic differential equation and martingale problem associated with mean vector. Also, we examine that if the operator related to this martingale problem is connected with Markov processes under certain circumstance, then this operator must satisfy the maximum principle.

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