Birth death chain Problem Markov chain Consider with Xn a State space with 91,2 fi i if j ki i qi else 0 where Pit Kiyo Wifi Qi 70 e Positive recurrent Find a chain Is the a Justify b the chain Is reversible pi Po Nail 1 to ai solve if Sof can we
IP with I Tri O ti the M C recurrent is positive CBigtheorem E Koti In tint In P seetransition diagram Depends on Tn Rtl TK in tuk FK g 2 kn i I Kti Nkt 3 Tk I 7 k i the 9k Truce Recursi To to To l Base condition IGeu.FR B.Dchain FromBn ecoh d a o tiz peg E3 r
Induct the recursive equation ob q i µi an AK fg 9h92 exercise 1 if MC P R is ther L In N K 0 a a a 1 Ee above the From true is
is tr L N I ra Positive Recurrent M C is So a To Az with Roth t L stationary prob to Z Also I tot q 1 50 1 stEi I b Reversibility check for Balance Egnation i P D
i Pfj if aipcis D hjCPG.si then M C is reversible In this prob I ripe I riuPh po l ti Wii 9 PiS fo his to pi 9 hit or Ni to Pi 79 fame
M So reversible is C fasych eck ili Conor EEE self remove loops remove duplicate edges the resulting graph if tree IS a c is reversible then M o_0 0 0 0 Line Graph Tree
is reversible he C Hoo 819
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