ON THE MARTINGALE PROBLEM AND SYMMETRIC DIFFUSION IN POPULATION GENETICS

  • Choi, Won (Department of Mathematics, University of Incheon) ;
  • Joung, Yoo-Jung (Department of Mathematics, University of Incheon)
  • Received : 2009.11.10
  • Accepted : 2010.02.17
  • Published : 2010.05.30

Abstract

In allelic model $X\;=\;(x_1,\;x_2,\;\cdots,\;x_d)$, $$M_f(t)\;=\;f(p(t))\;-\;\int_0^t\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we define $T_tf\;=\;E_{p_0}^{p^*}\;[f((P(t))]$ for $t\;{\geq}\;0$ for using a new diffusion operator $L^*$ and we show the diffusion relations between $T_t$ and diffusion operator $L^*$.

Keywords

Acknowledgement

Supported by : University of Incheon

References

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