user366312
Gold Member
 62
 2
 Problem Statement

Consider the transition matrix
##
P = \begin{bmatrix}
1p&p\\
q&1q
\end{bmatrix}
##
for a general twostate chain ##(0 <=p; q <= 1)##.
(a) Find the limiting distribution (if it exists) if ##p + q = 1##. (I can do this myself)
(b) Find the limiting distribution (if it exists) if ##p + q \ne 1##.
 Relevant Equations
 What I understand is, there is a matrix ##P^n## (where ##n = 1,2,3,...##) which tends to reach an equilibrium. I have to find that matrix.
2nd one is considerably hard to compute ##P^n## using simple matrix multiplication as the given matrix ##P## is cumbersome to work with.
Also, I need to know how to test a matrix to find if that matrix has a limiting distribution.
So, I need some help.
Also, I need to know how to test a matrix to find if that matrix has a limiting distribution.
So, I need some help.
Last edited: