Korean J. Math.  Vol 22, No 1 (2014)  pp.29-36
DOI: https://doi.org/10.11568/kjm.2014.22.1.29

On the martingale extension of limiting diffusion in population genetics

Won Choi


The limiting diffusion of special diploid model can be defined as a discrete generator for the rescaled Markov chain. Choi( \cite{Choi2} ) defined the operator of projection $S_t$ on limiting diffusion and new measure $dQ=S_t dP$. and showed the martingale property on this operator and measure. Let $P_\rho$ be the unique solution of the martingale problem for $\mathcal L_0$ starting at $\rho$ and
$\pi_1 ,\pi_2 , \cdots, \pi_n$ the projection of $E^n$ on $x_1 , x_2 ,\cdots, x_n$. In this note we define 
$$ dQ_\rho =S_t dP_\rho $$
and show that $Q_\rho$ solves the martingale problem for $\mathcal L_\pi$ starting at $\rho$.

Subject classification

92D10, 60H30, 60G44


This research was supported by Incheon National University Research Grant, 2013-2014.

Full Text:



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