ON THE MARTINGALE EXTENSION OF LIMITING DIFFUSION IN POPULATION GENETICS
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The limiting diffusion of special diploid model can be defined as a discrete generator for the rescaled Markov chain. Choi([2]) defined the operator of projection S_t on limiting diffusion and new measure dQ=St dP. and showed the martingale property on this operator and measure. Let Prho be the unique solution of the martingale problem for mathcal L0 starting at rho and pi1 ,pi2 , cdots, pin the projection of En on x1 , x2 ,cdots, xn. In this note we define dQrho =St dPrho and show that Qrho solves the martingale problem for mathcal Lpi starting at rho.
Abstract
The limiting diffusion of special diploid model can be defined as a discrete generator for the rescaled Markov chain. Choi([2]) defined the operator of projection S_t on limiting diffusion and new measure dQ=St dP. and showed the martingale property on this operator and measure. Let Prho be the unique solution of the martingale problem for mathcal L0 starting at rho and pi1 ,pi2 , cdots, pin the projection of En on x1 , x2 ,cdots, xn. In this note we define dQrho =St dPrho and show that Qrho solves the martingale problem for mathcal Lpi starting at rho.
참고문헌 (3)
- 최원, "On the limiting diffusion of special diploid model in population genetics", 대한수학회보, 42(2), pp.397~404 (2005), 대한수학회
- 최원, "On the martingale property of limiting diffusion in special diploid model", Journal of Applied Mathematics and Informatics, 31(1), pp.241~246 (2013), 한국전산응용수학회
- A.Shimizu, "Stationary distribution of a diffusion process taking values in probability distributions on the partitions", Proceedings of a Workshop held in Nagoya, pp.100~114 (1985)