Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE MARTINGALE PROPERTY OF LIMITING DIFFUSION IN SPECIAL DIPLOID MODEL

  • Choi, Won (Department of Mathematics, University of Incheon)
  • Received : 2012.08.21
  • Accepted : 2012.10.16
  • Published : 2013.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

Choi [1] identified and characterized the limiting diffusion of this diploid model by defining discrete generator for the rescaled Markov chain. In this note, we define the operator of projection $S_t$ on limiting diffusion and new measure $dQ=S_tdP$. We show the martingale property on this operator and measure. Also we conclude that the martingale problem for diffusion operator of projection is well-posed.

Keywords

References

  1. W.Choi, On the limiting diffusion of special diploid model in population genetics, Bulletin of the Korean Mathematical Society, Vol 42, No 2 (2005), 397-404. https://doi.org/10.4134/BKMS.2005.42.2.397
  2. W.Choi and D.H.Choi The application of stochastic differential equation to population genetics, Bulletin of the Korean Mathematical Society, Vol 40, No 4 (2003), 677-683. https://doi.org/10.4134/BKMS.2003.40.4.677
  3. S.N.Ethier and T.G.Kurtz, Markov processes: Characterization and Convergence, Wiley, New York (1993).

Cited by

  1. ON THE MARTINGALE EXTENSION OF LIMITING DIFFUSION IN POPULATION GENETICS vol.22, pp.1, 2014, https://doi.org/10.11568/kjm.2014.22.1.29