[機統] martingale(wright-fisher)
let Xn be the wright-fisher model with no mutation defined in example 1.9.
a) show that Xn is a martingale and use thm 5.14 to conclude that
P(Vn^Vo)=x/N
b)show that Yn=Xn(N-Xn)/((1-1/N)^n) is a martingale
c) use this to conclude that
(N-1) <= x(N-x)(1-1/N)^n <=N^2/4
-----------------
Px(0<Xn<N)
我算出a跟b
但想不到怎麼算c
完全不知道要怎麼下手
所以想請教一下板友c要怎麼做
謝謝
example1.9 在這裡: http://ppt.cc/PuO1
thm 5.14 是 suppose Mn is a martingale and T is a stopping time with
P(T<infinity)=1 and |MT^n|<=K for some constant K. Then E(MT)=E(M0)
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