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(1 + εt)t
) Pr{Xt−1 = i} − 1
t
∣∣∣∣+ 1 2
∣∣∣∣Pr{Xt= t} − 1 t
∣∣∣∣ (4.57)
≤ 1 2
( 1− 1
(1 + εt)t
) t−1∑ i=1
∣∣∣∣Pr{Xt−1 = i} − 1 t− 1
∣∣∣∣ +
1 2
t−1∑ i=1
∣∣∣∣(1− 1 (1 + εt)t
) 1
t− 1 − 1 t
∣∣∣∣ + 1 2
∣∣∣∣Pr{Xt= [...] q) = 1 2
∑ ω1∈Ω1,ω2∈Ω2
|(q1(ω1) + δ1(ω1))(q2(ω2) + δ2(ω2))− q1(ω1)q2(ω2)| (2.45)
= 1 2
∑ ω1∈Ω1,ω2∈Ω2
∣∣∣∣δ1(ω1) ( q2(ω2) +
1 2 δ2(ω2)
) + δ2(ω2)
( q1(ω1) +
1 2 δ1(ω1)
)∣∣∣∣ (2.46)
≤ 1 2
∑ ω1∈Ω1,ω2∈Ω2 [...] F̃i+1 and by Proposition 2.2.12, we have
H(F̃i+1(1)|F−(i+1), T1,i−1) = H(Fi+1(F̃i(1))|F−(i+1), T1,i−1, F̃i(1)) (3.113)
= n∑ p=1
Pr{F̃i(1)=p} ·H(Fi+1(p)|F−(i+1), T1,i−1, F̃i(1)=p) (3.114)
= n∑ p=1
Pr{F̃i(1)=p} …
