Re: [閒聊] 這是應機吧
※ 引述《johnsonla (johnson)》之銘言：
: Disscussion about the definetion of peroid
: please check all of the "<=>". XD
: note from textbook p204:
: State i is said to have period d if Pii^n = 0
: whenever n is not divisible by d,
: and d is the largest integer with this property
: <=> d(i) = max{ d | n 不被d整除, for all n>=1} st Pii^n = 0
: But I have a little confusion as n = 1,
: so consider that
: <=> Pii^n > 0 whenver n is multiple of d,
: where d is the gcd of n.
: <=> d(i) = gcd{ d | n被d整除, for all n>=1} st Pii^n > 0
: guess:
: 如果Pii是aperopdic
: 矩陣P 對角線的值Pii要大於0
NO.
你應該是說如果state i 是aperiopdic則Pii>0吧..
ex.A DTMC with state space S={0,1,2}
The transition matrix
0 1 2
0 0 1/2 1/2
P= 1 1/3 1/3 1/3
2 1/3 1/3 1/3
state 0 是 aperiodic, 但是P00=0,
(if d(i)=1,then state i is aperiodic,無週期的意思)
以下是跟guess無關的truth.(maybe..xd)
因為periodicity is a class property
所以在one-step transition matrix中,
只要有一個Pii>0 (If the MC is irreducible)
則這個DTMC的transition matrix是aperiodic
--
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◆ From: 59.115.230.113
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10/20 21:23, , 1F
10/20 21:23, 1F
※ 編輯: clskys 來自: 59.115.230.113 (10/20 22:13)
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10/21 21:38, , 2F
10/21 21:38, 2F
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