Winter 2010
Pstat160a
Handout MC#3
Classification of states
1. Communication classes, irreducibility:
2 states
i, j
communicate if the process can go from
i
to
j
and from
j
to
i
in one or more steps.
The set of states
that communicate with each others are in the same communication class.
The chain is irreducible if there is only one
communication class.
2. Transience/recurence:
A state
i
is recurrent if the probability to come back to
i
(so starting from
i
) is 1, it is transient if this probability is
<
1.
Transience and recurrence is a communication class property, so we say that a class is recurrent (or transient) if its states
are recurrent (or transient).
3. Period:
The period of a state
i
is the greatest common divisor
d
of
n
such that
P
(
n
)
ii
>
0. That is
d
≥
2 if
P
(
n
)
ii
>
0 on if
n
=
kd
for any
k
large enough. So if
P
ii
>
0
, d
= 1. Periodicity is also a class property.
4. Examples:
P
=
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '10
 bonnet
 Greatest common divisor, Mutator method, C Sharp

Click to edit the document details