# how to calculate limit of P(Xn = j | X0 = i) in markov chain?

1.

lim N ® ¥ [1{X1 = j} + 1{X1 = j} + … + 1{XN = j}]/N = 0

What is N? how it limit to zero? and what do 1 in 1{X1 = j} represent?

/N must be 0, no other choice, any other example to show limit this is non-zero?

2.

would like to calculate lim pij(n) = lim P(Xn = j | X0 = i)

in my past experience P(x) is just a distribution, how to get this if just know counting such as number of happened? and how to count total happened or number of ways from i to j in graph for denominator for the probability? maybe i misunderstanding it, so ask this

how to calculate P(Xn = j | X0 = i) when just know the graph

if markov chain [6] in above link

do it need to know all probability of 1 -> 2, 2-> 3, 3->4, 3-> 1, 4-> 3?

if so, please use example in http://www.math.ucla.edu/~pejman/intro2prob/LiveMeeting11.pdf

i use one of example in above if 1 ---p=0.5---> 2 ---p=0.5---> 3
and extra path 1 ---p=0.3---> 3

does P(Xn = 3 | X0 = 1) = 0.5*0.5 + 0.3 ?

if limit above, there is no N in it? which case show limit is zero

is end state has an arrow point to itself then lim P be infinity?

if so, does it mean that a state consecutively happened twice or above, then lim P is infinity?

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For some basic information about writing math at this site see e.g. here, here, here and here. – user17762 Jan 9 '13 at 5:29
Are you familiar with $\LaTeX$ at all? It would make this appear clearer (or at least more aesthetically pleasing). – emka Jan 9 '13 at 6:13
After you will have made your question readable (and not requiring stuff on external sites to be understood), you might want to get hold of a textbook on the basics of Markov chains, say the very first chapters of Norris, and to read it. – Did Jan 9 '13 at 6:13