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(α,β) n (1− 2x) =
(2n+ α + β + 1)(α2 − β2) + (2n+ α + β)3
2(2n+ α + β)3
P (α,β) n (1− 2x)
−2(n+ 1)(n+ α + β + 1)(2n+ α + β)
2(2n+ α + β)3
P (α,β) n+1 (1− 2x)
−2(n+ α)(n+ β)(2n+ α + β + 2)
2(2n+ α + β)3
P [...] 2k(σ2 + k) − γσ2
2k +
4kγ2(1− γ)
σ2 + 2k ,
V2 = −4k2γ2(1− γ)2
(σ2 + 2k)2 ,
V3 = − σ4
(σ2 + k)(σ2 + 2k) .
(c) The stationary distribution is the limiting distribution, and is given by the Beta distribution [...] A(t, T ) = exp
2kθ
σ2 ln
2h · e σ2(T−t) h−k
2h+ (k + h)(eh(T−t) − 1)
=
2h · e σ2(T−t) h−k
2h+ (k + h)(eh(T−t) − 1) .
With
σ2(T − t) h− k
= 2σ2(T − t) 2(h− k)
= (h2 − k2)(T − t)
2(h− k) =
(k + h)(T …
