Nail 1 to ai solve if Sof can we IP with I Tri O ti the - - PDF document
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
Problem
Birth death chain
Consider
a
Markov chain
Xn with
State space
91,2
with
fi
i
ki qi
if j
i
else
where
Kiyo
Qi 70
Pit
Wifi
e a
Is the
chain
Positiverecurrent Find a
b
Is the
chain
reversible
Justify
Po
pi
ai
1 to
Sof
if
we can
solve
IP
I
with
Tri
O
ti
the
M
C
is
positive
recurrent
CBigtheorem
E
Koti
In
In tint
P
seetransitiondiagram
Depends on
TK in
FK g
Tn Rtl
2
tuk
Tk
I
k i
kn i
7
I
Kti Nkt3
Truce
the 9k
To
To
l
to
Recursi
Base condition
B.Dchain FromBn ecohd
peg
a o
tiz
E3
r
Induct
the
recursive
equation
i
an
9h92
AK
exercise
1
if
MC
is
P R
ther
In
L
N
K 0
a
a
a
1 From
the
is
true
is tr
ra
L
N
So
M
C
is
PositiveRecurrent
To
a
Az
stationary prob
with Roth t
L
Also
tot
to Z
q
I
50
1
1
b
Reversibility
i
check for
Balance Egnation
P
D
Pfj
i
hjCPG.si
then
M
C is
In
this
prob
reversible
I
riuPh
po
l
9
fo
to pi
his
9
hit
Ni
to
Pi
M
C
is
reversible
ili
EEE
remove
loops
remove
duplicate edges
the resulting graph
IS
a
tree
then
M
c is reversible
Line
Graph
Tree
he
C
is
reversible
Hoo 819